I think kids need to feel somewhat in control of their situation. By definition in a bug out, there is very little control.
Keeping kids entertained and engaged and above all keeping them safe are my priorities.

Items like the whistle (on a lanyard) are great. Have a practice session or two where they can practice blasting their whistle …

A chemical glow stick has the benefit that it will glow all night, as a comforting night light. Just be sure she knows how to use it.
A small LED light is also great because it can illuminate a task area. Windup and solar lights have the benefit that they will not run out, but batteries have that instant effect. I went for a small windup because the kids can play indefinitely with it and not waste the battery. I have battery lights I can choose to share with them if I want them to have them. (I think it gives them a bit of control – control of their light)

A favourite book, or a copy of the book.
Family photos – DW made a small album which included family groupings and a few individual shots too. Kids love photos of their family and friends.

If she has a favourite character, then consider some colouring books or stickers etc which feature that character (this may change over time). Blank paper is always good.

Definitely a cuddle toy, once again, if they have a favourite consider getting another of those characters, and Hey ! … you could always make up your own ? How about inventing Doug the Survivor Dog ?
In the event of getting lost, Doug sits down and blows his dog whistle ? …. Hey I may write a book ….

A refillable water bottle is good, but you could consider a small juice drink too. Comfort food ?

Include some kind of instructions. Not sure if your kids can read as yet, but some pictures and simple works may be appropriate.

You can consider including some information with their name, your name and details etc. as well as some family or trusted friends who may be away from the bug out area.
If they do become separated from you, consider what information may help authorities reunite you ?
Her photo of mummy (and your photo of her) may assist in this process.