I am a pharmacist, and I can tell you the Bactrim has been around for a really long time, and many, many people use it with no problems. MRSA is very serious and very difficult to eradicate, so please, please give your daughter the medicine as prescribed. There are very few oral antibiotics that work for MRSA, and this is one with a long track record. I'd much rather have my child on an older, proven med than on one that has only been out a couple of years. You can be relatively sure that with an older medicine, they have found any of the serious side effects by now and wouldn't prescribe it if the benefit didn't outweigh the risk.
The biggest thing with Bactrim or any sulfa drug... watch out for sun exposure, as it can make you much more susceptible to sun burn, and drink lots of fluids. Since you're in Florida and it's still warm, be sure she is wearing sunscreen. Other than a possible allergy, which will show relatively quickly, most people tolerate sulfas well.
Good luck. I encourage you to ask your pharmacist if you still have concerns. Googling can really get you in trouble in the sense that a little information ... without the medical background to truly understand what you are reading... can really be scary. I have done that, too, and ended up getting upset over nothing. Try to resist looking, you will drive yourself crazy.