OK, first thing: don't panic! Disney is the most accessible place I've ever been, and is wonderfully easy to navigate with wheels. As your daughter is so young, I would suggest you go and talk to Guest Relations at the first park you go to, where you will be issued with a Guest Assistance Card (GAC). This is basically a card that tells Cast Members what your needs are, if they aren't obvious. For you, the only thing you'd really need is a "stroller as wheelchair" GAC, to allow you to take her stroller into lines and buildings where you couldn't normally. You don't need any medical notes etc for this, you just need to be able to briefly explain your daughter's needs (e.g. she can't walk or stand for long periods, so will need to take her stroller into queues etc). For more information on the GAC, see the
FAQ thread.
Most of the rides now are mainstreamed, which means wheelchairs go most, or all, of the way through the regular line, and are pulled off near the end of the line to board elsewhere (often the exit). For those few attractions that have alternative entrances, the CM at the attraction door will show you where to go. Be warned that it does take longer to get through some ride lines with a wheelchair, than it would in the standard line / boarding area, but it is worth it if it helps your daughter!

Whichever entrance you need to use, you don't need to separate your party, unless there are more than 6 of you travelling (including your DD). Some of the shows only have one seat next to the wheelchair space, so you might have to split up then, if she was staying in her stroller. However, she'll probably be more comfortable and have a better view if she sits in the theatre seats, as strollers are usually fairly low.
If she's having a good day and feels like walking, that is perfectly fine, just park the stroller in the stroller parking and go have fun! Be warned though, that some rides have a very long walk through the line (even if there aren't many people in the line), and that you may end up waiting longer than the predicted time if the ride breaks down or has problems. Rides such as Soarin' and Kilimanjaro Safaris have a long walk from the entrance of the line, to the boarding area, so take the stroller through for them.
Hope this helps! Wishing your daughter a speedy recovery!
