HP's "300w power supply" is a bit vague, but those gpu's consumptions are actually very low.
I think you'd be allright
As a general rule of thumb you should look to upgrade your PSU whenever you start adding additional or new performance components to a prebuilt, mass-market PC. Many off-the-shelf desktops come with incredibly cheap, unreliable PSUs that lack even failsafe mechanisms for catastrophic failure (i.e. if it blows up, it takes the whole computer with it). Wattage means very little if the PSU isn't actually working as efficiently as it should.
You can buy decent (80+ bronze) 350-500W power supplies for extremely cheap. In my book the extra cost is well worth the protection and reliability and you'll then have plenty of headroom to work with. On the other hand, OP will likely be fine as you said... for a time, at least. I personally wouldn't be willing to take the risk on my only gaming rig, but I guess to each his own.
To answer your direct question, OP, a 6750 would be a worthwhile upgrade for your current system. But why buy a laptop for gaming? I don't mean to pry, but for a similar price you could build a much better gaming desktop (your current PC isn't a great candidate for total overhaul/upgrade, unfortunately). Why not put the meantime upgrade money into that?