First off, cover the mattress with plastic. Then go to the pet store and get two products. The first are puppy training pads, which have the same chemical in them as diapers, but they're flat. You can put these under your child (either under the sheet, or over it if you think it will stay in place - ie. she's not a big mover). The other product is something called Nature's Miracle, which is an enzyme that cleans up urine. There are lots of other products on the market, but that's the one that works best for me. Then, let her sleep in underwear! Clean-up will be easy with the training pads, but if for some reason she misses, clean-up isn't bad, then, either!
My three-year old slept in underwear, so I don't think she is too young. Then again, children have accidents until they are much older, so you have to be prepared to do some cleaning. She'll probably learn much more quickly while wearing underwear than diapers, so this is a great step.
Good luck!