I'd budget a little money to get your daughter something she really wants that is parks-only. You can get an idea of parks-only things by browsing regular Disney merchandise in other stores and at
Disneystore.com. Otherwise, get her some cheaper things from places like the dollar store, Wal-Mart, Target, or Five Below. To add more punch to this, you can hide them and pull out a new thing every day.
Mickey ears are often adorable, but expensive in the parks. You can find tutorials to make your own on Google, or sometimes buy ones from Etsy for a decent price.
Bring something to hold water in and refill them when needed. If your daughter likes sugary drinks, bring some instant drink packets as treats. As someone else said, any restaurant will give you iced tap water if you ask.
Any Photopass photographer will also take pictures with your camera if you ask nicely and have it ready to go. Just keep the Photopass card and keep asking, since they more or less MUST also do the Photopass stuff. Be sensitive to how long you stay for photos, though, as sometimes those lines can pile up.
Download the Aurasma app on your phone before going. There are places in the park, particularly for Frozen, that you can get some interesting shots for free. Since you have a little girl, I assume she's into Frozen!
There are definitely foods that can be split in the parks. If you're not sure what a portion size really looks like, just back up and watch what others are getting. Stick to counter-service unless you are splurging on a character meal. If you want to guarantee a character interaction in comfortability, you might want to consider a character breakfast. Otherwise, line up early and have some activities for your daughter while you wait.
Pack some snacks for use in the parks. Bring a few things that will be treats for your daughter. Commonly sold in the parks are churros, candied nuts, popcorn, mickey rice krispy treats, and mickey ice cream. See if you can head off potential "I WANT THAT" moments by packing something similar in a 'dressed up' package.
If you are heading to Epcot, there are kid stations in every pavilion. They have a coloring activity and stamps for each country. You can add to this by making your own passport and asking a cast member in each country to sign it with a "Hello!" or "Welcome!" and your child's name in that language (for places like China or Japan). These things are all completely free.
When in the Magic Kingdom, go to the fire station (to the left of the entrance gates, where the parades start) and ask to play Sorcerers of the Magic Kingdom. Even if you don't play much, the cards are pretty cute and collectible, and she will definitely get a kick out of watching a few portal animations. People like me will also probably 'trade' with your daughter (I keep a lot of duplicates to give to kids who want them).
Remember to ask for 1st Visit! pins when you get to your resort, or at any guest services location in the parks. Especially for your daughter, cast members will be able to use this as a conversation point and are more likely to ask her about her day, if she's seen so-and-so, or sometimes even sprinkle a little more pixie dust her way. Don't expect it to do magic, but be happy if it does!
As someone else mentioned, cheap glowsticks or light toys could save you a lot of money by bringing them as opposed to buying them in the parks. If you find a good deal, you can teach your daughter the merits of sharing by giving a couple glowsticks away to other kids.
Also in Epcot there is a Coca Cola soda fountain with drinks from around the world. It's a good place to taste something unusual and be inside for a while. In the World Showcase there is an Agent P secret mission game (not sure if she's old enough for this). Innoventions sometimes has activities for kids to do and take home-- I remember being there once and seeing some kids making paper and then stamping it when they were done. All of this for free!
Don't forget to make your FP+ decisions for anything you decide must be done. At 4, she might not want to see all the evening light shows, but I'm sure she'll be impressed by at least one. If doing this, make sure to check out the fireworks viewing threads on the boards, which have great tips, and take a nap earlier in the day to avoid crankiness.
As for must-dos, it really depends on those involved. What kinds of park-goers are you? Do you want to do all the classics? Do you want some things that might require baby-swap? Does your daughter have a favorite character or movie?
