The Lowepro Passport Sling is a great, low cost bag that doesn't scream "camera bag". It's got protection for the camera plus lens attached and room for one more lens. I recommend you check it out.
The neck strap is definitely worth replacing if you think she'll have the camera hanging off her neck for extended periods of time. I've found that if you use a sling-type of bag that you don't use the neck strap that often since you can just keep the camera in the bag when you're not snapping a shot. Thicker, more comfortable straps come at the cost of more bulk hanging off your camera. I personally like to have a comfortable strap on my camera, but my wife's D5100 has had the stock strap on it since Day 1 and she hasn't complained. I've even asked her if she wanted me to get her a new strap, and she was indifferent at the thought of it.
We've discussed the need for a second battery in the past on this forum. Most people will say a second battery is a must. I completely disagree with that. As long as you are good about charging the battery before long shoots, a second battery is not necessary at all. It can be useful for people who go camping or go to places that don't have access to power to charge overnight. I've NEVER run out of juice while shooting for very long periods of time, but I'm also very good about charging the battery whenever I've used it extensively.
Edit: The battery should last over 500 shots per charge. You can gauge your needs based on this. 500 is really conservative too, but even thinking about taking 500 shots in one shooting session is pretty ridiculous.
You should pick up the 35mm 1.8G prime lens. It's basically the sharpest lens you can buy for that camera while also being the most affordable. Because of the very large aperture, this is the lens that will offer that blurred out background that all new dslr users covet. The large aperture also offers great low-light night performance (the 18-55 will suffer indoors without a ton of bright lights on).