I think it's completely doable.
It just really depends on the pattern you want to use. I would avoid anything with pintucks or gathers for a first project. A simple slip dress or A-line dress should be just fine. Go looking for patterns, several of the big pattern houses rate the patterns by difficulty level, look for that. And be sure that the direction sheet is in the envelope. Pick a pattern that you can reuse again for other purposes - like you'll make something a little nicer for her b-day, but then maybe you make some play dresses out of it, too.
Read the instructions all the way through first and post here asking any questions you have BEFORE you start. Allow yourself plenty of time to do this the first time. And I'd probably start with a play dress first out of a cheaper fabric. Once you know you can do the pattern and have worked out any kinks, then work with your nicer fabric.
Another thing to think about is fabric - don't pick anything stretchy or slippery, they make life much more difficult. Stick to a pretty woven cotton.