Wildcard, contrary to what some people in here are suggesting, I seriously doubt you have ANY problems with your catlytic converter (or as my grandfather calls it, the catholic converter).
Catlytic converters are simply "afterburners." They reignite the exhaust gases to burn your fuel more completely.
If your catlytic converter is not functioning properly, it will not reburn your exhaust gases, and the result will be that your emissions will be more polluting to the atmosphere. This will not harm gas mileage in the slightest. This reignition of your exhaust gases produces lots of heat, but it is completely wasted. No cars try to recapture this "extra" energy and use if for making the vehicle get better gas mileage.
The only other possible problem relating to the catlytic converter is that some of the pieces inside have broken loose and are somehow impeding the flow of exhaust. Pieces do occasionally break loose inside them, but they aren't supposed to be designed such that they could impede exhaust flow. That is, the aren't supposed to be shaped such that they clog up the flow.
Even so, I have heard of people claiming their exhaust systems "exploded" where a bunch of crap (including sparks and stuff) flies out of their tail pipe after the catlytic convertor breaks down and peices clog up the exhaust system.
The fact is, exhaust gases have TREMENDOUS pressure if they cannot get properly exhausted to the atmosphere. Try this experiment for kicks: place a potato up the end of your exhaust pipe while your car is turned off. Then, try to start the car.
If may have some difficulty getting started, but the potato should come flying out of there at some pretty extreme velocity when it does. Of course, don't try this experiment with anyone standing behind the car... Duh...
Anyways, if your catylitic convertor was somehow impeding the flow of exhaust, chances are the backpressure alone would be plenty to open up the clog by exhausting the offending material.
So...... Simply, your catlytic converter is NOT your problem. If it was, you would also hear some noise coming from below your vehicle while it was running as well (which you didn't describe). Of course it is concievably possible that your exhaust system is only partially clogged (hence poor MPG's, low performance, but no "explosion" removing the clog), however, I find that MOST unlikely. There are far better explanations than the catyltic converter that would cause low MPG's... Not to mention the fact that catyltic converters never die after driving with them a mere 15K miles. I've had one get loose parts inside after about 101K miles, but NOT 15K. That is practically a brand new car/catylitic converter.
Others in this thread have mentioned broken sensors (ex: Oxygen sensor). Again, I am skeptical that this is your problem. All of your various sensors are wired directly up to your "ECM" (engine control module... aka, car "computer". If any one of your sensors are malfunctioning, they will be providing the ECM (car computer) wrong information. Normally when a sensor is not working properly, it will be reporting information to the ECM that is WAY off of what it should be. If this is the case, the ECM is smart enough to know that something is not right and will automatically trigger your "Check Engine" light to illuminate on your intrument cluster.
Since you didn't describe the check engine light to be turning on, I can presume that this isn't your problem (most likely).
Of course, if a sensor is only "a little wacked" it could theoretically report mis-info. to the ECM, but the ECM would determine it to be within normal parameters and operate based on that info anyways without realizing that it is faulty. But again, that is fairly unlikely considering the other possibilities that could be ailing your vehicle. Oh yeah, also sensors will almost never die within a mere 15K miles after getting out of the factory. They normally take a fair amount of abuse...
Things I would check to see what is wrong with the vehicle:
1. Compression test on all cylinders (is that a 4 banger or 6 banger or what? I don't know what Camry's normally have). Basically, this tests to see how well all of your cylinders seal up and can contain an explosion. This test will reveal LOTS of information if you have a problem such as a blown head gasket (sounds like a possiblity to me based upon what you describe), or not properly sealing valves, or somehow not properly sealing piston rings. IMO, this is most likely one of your problems.
Tell me. Did you ever make your car overheat lately just before the problems with MPG's began? If you run your car too hot (due to not enough water, not enough oil, broken water pump, or whatever else), you can warp you head and possibly engine block. This results in a "blown head gasket". Once blown, your cylinders will ingite each other when they aren't supposed to. This could definitely cause the drop in MPG's. Not to mention low performance...
Most likely a blown head gasket will NOT trigger the Check engine light to illuminate (IMO). No Camry engine I am aware of has pressure sensors inside the cylinders. For that matter, I've never heard of such a thing (although it might exist in racing cars or something, I donno)...
Anyways, since you don't know much about cars, you'll have to take it to a repair shop for them to run this test. All your cylinders should be within 15 PSI of each other (that is, your highest compression cylinder should be no more than 15 PSI higher than your lowest compression cylinder), and should be within the specifcations listed in your vehicle's shop manual. You'll probably have to buy one of these to find that info out.
2. I'd check to make sure all your cylinders are getting the spark properly. Check all spark plugs for proper gapping. OTOH, I doubt this is a problem since your car is so new and has so few miles on it. Even your factory original spark plugs should be gapped fairly well (that is, useable) after a mere 15K miles. Make sure your spark plug wires are fully attached to the spark plug ends on the engine.
Other than that, there isn't a whole lot I can suggest without a WHOLE LOT MORE INFO about your car. I need info such as: how is performance, has it dropped, is there water in the oil (oil would look milky/whiteish), is there oil in the water, is your car fuel injected or carberated (sp?) (almost certainly fuel injected, but I know nothing specific about Camry engines), do you ever smell fuel inside the engine compartment, did the check engine light ever turn on, does the car make any unusual noises, how does the exhaust look, is it smokey/white looking or anything, does your exhaust smell at all like raw gasoline, and pretty much anything else relevant relating to your car.
But be forewarned. Normally a large drop in MPG's indicates a serious problem with your car. If you are very lucky, you'll get by with something very cheap like new spark plugs. But normally, large drops in MPG's indicates something very serious such as a blown head gasket/burnt valves. Those types of repairs easily range up into the several hundred dollar+ range to repair... Unless of course you educate yourself up on auto mechanics and learn how to fix it yourself (something I would recommend to anyone).