This question seems to be asking about two actions. One is someone 'going through' a backpack. The other one is 'going through the things found in a backpack'.
Stop going through my things
fits the second case.
As does the expression you provided:
Stop searching through my stuff
User3169 has provided a highly idiomatic expression:
Stop digging through my things
CopperKettle has provided the useful verb rummage (which is also a noun):
Stop rummaging (through) my backpack
Also, stop messing with my things/stuff is similar, but it is broader in meaning.
You can also say
Get your hands out of my backpack
Leave my stuff alone
Find your own toys to play with
For variety and vocabulary expansion, you might want to be aware of
Stop rifling through my things
but rifle as a verb means to go through something quickly in order to steal something, and we wouldn't generally use that for a toddler.
Note: I have not used a period after any of the italicized examples, because I want to leave open the fact that you can add , toddler's name or something else the end of each one.
Stop messing with my stuff, lovey dovey.