I may be in the minority, but I'd say, when in doubt... don't.
My children were ages 4 (daughter) and 6 (son) at the time of our first WDW visit. We toured up to 5 hours at a time every morning and then again for another 5-6 hours every evening (with a nap break every afternoon and frequent restroom/snack breaks throughout the day), all on foot, and both kids did beautifully -- no whining to be carried, and not so much as a blister on their feet. (We did take care to put them in well-broken-in athletic shoes in the morning, and hiking sandals for our more relaxed evenings, so they were properly equipped for all that walking.) Granted, both of my kids are tall for their ages, very energetic, and in decent physical shape, and they were getting a 1-2 hour nap almost every afternoon. If your daughter is of typical-or-better size and health for her age, and if you're not planning to stay in the parks all day, from rope drop to closing, there's no reason she should
need a stroller, and you'll be able to navigate much more freely without it. (That being said, just because she doesn't
need it doesn't mean you might not still want to bring one, for reasons discussed by others above - just weigh the pros and cons ahead of time, keeping in mind that having a stroller means having to find places to park it every time you visit an attraction, and having to continually unload it and fold it up on most Disney transportation.)
The only "strolling" my children did was this kind...