I have the same issues-4 and 5 year olds. I have a lot of the stuff they would need in the basement. It has long been my contention, that most people planning on bugging out are planning to do the wrong thing. Unless you have a place to go, you're just refugeeing it and I would hate to ever end up in that position with my kids. My plan is/has been to stay in until the very bitter end. I know that bugging out is the trend and much of the gear market involves being prepared for a disaster by having a fully stocked backpack next to the door. The only bag I have is for getting me home, not leaving it. For the life of me, I cannot fathom a situation in which I would scream at the kids for everyone to grab their backpacks and run out the door in under a minute. Even people in Katrina (the most pointed to recent bugout event) had DAYS to pack.
I say all that to say, that my suggestion would be to stock up on stuff that would allow her to survive at home, rather than concentrate on walking around with a little kid (a la THE ROAD). One thing I've stocked up on that may seem unconventional but I think it would come in very handy are crafts, games, books, etc that will keep my kids busy. Imagine a week where the kids are cooped up with little to do but see their parents worry and not fully understand why they can't go outside or go play or whatever. Keeping you mind occupied in a survival situation is a very good thing to do.
As far as clothes, I have long been a fan of Patagonia stuff. Expensive as heck, yes, but they regularly have 40% off sales and their stuff I've bought has lasted forever. They have a lot of kid's cold weather gear. I would not hesitate to buy the smallest women's size and fold, pin, hem, whatever was needed to fit.
We have a section in what my kids have begun calling the Panic Room that is just for them. Getting them involved into preparedness has changed the way their little minds look at things and they don't worry about things as much. For example, my daughter used to get really scared during thunderstorms, especially if the power went out. Now, they know they just go to the basement, get in the stock of candles and get a game out to play by candlelight. Now, it's just a different experience, not a bad experience.
When stocking up on food, make sure you get some stuff that they not only like but REALLY like, like some sugar treats or something. That stuff normally has a long shelf life and a little bit of it, used sparingly helps keep up the kid's spirits. Something that may come in handy for lifting the parent's spirits too, to see their kids are doing well.
Just my two cents based on my knowledge set now.
