As you can see, I moved this thread to the gear section.
It sounds like your daughter is definitely ready to step up to the next level of gear quality, but that she's not quite ready for top end gear yet. You want to find gear that has better materials than your average Sportmart stuff. The easiest way to do this is to visit your local snowboard shops. They are going to have better gear and better advice. Strangely enough, even with better quality gear, she's going to be quickly reaching the stage where she's going to wear out even the good stuff. So don't be shocked if a strap needs to get replaced next year or she's ready to trade up again in another year or two.
The most important thing to be careful of is to not get a board that is too stiff. You can feel the difference in stiffness by holding the board upright and trying to push the middle of the board, but this is something a shop can give you the best advice on. A stiffer board than what she had will improve her riding, but going to stiff is going to stifle it. It's a little hard to read the specs on a board and know if a wood core is better than a foam core is better than having a metal layer inside or what quality ptex is used for the base, but in general, the higher the list price, the more quality is in the board and the better it will perform. For some people, the graphics on the board are important too. For certain, ugly graphics can spoil the experience. Of course, perceptions of ugliness and coolness may vary. You may need to consult an expert on this (i.e. your daughter).
Two big things to consider with bindings are comfort and ease of use. If at all possible, bring in your boots and try the set up out in a store. Another advantage of using a shop is that you can ask them to help tweak the binding setup for the best fit. Sometimes it helps to offset the heel cup for a tighter fit. Make sure that you also learn how to adjust the highback forward lean. Make sure that you have the straps adjusted so that they ratchet tight into the middle of the strap vs too long or too short.
Although you've not told the story of the old board, one thing to make sure of is that your daughter has a cable lock to secure her new board while she's on the mountain. Don't forget to get a stomp pad. Ask your daughter whether she wants it in the middle or positioned towards the back foot. She should carry a snowboard tool for emergency fixes. She should also have helmet so that she can safely head butt the guys after successful tricks in the park. So as long as you're at it, get all the extra stuff too.