No, if you were to do what you're thinking, you'd have to pour at least a 4 inch thick slab of concrete before it would be strong enough to walk on without cracking (with dirt under it).
New concrete won't stick to old concrete. You basically need to glue the new concrete to the old stuff.
So, what I would do is paint a latex or epoxy "concrete bonding agent" onto the old uneven concrete surface, and then spread a thin surface coat of concrete over that same area. The concrete bonding agent will glue the new wet concrete to the old hard dry stuff.
In fact, if whomever poured the concrete into the kid's wading pool didn't use a concrete bonding agent, you could probably pull the concrete out of that wading pool with a back hoe. Or, maybe jackhammer it into pieces and remove the pieces from the wading pool.
If it wuz me, I'd hire a concrete contractor to do this work for you. That's cuz any mistakes you make pouring and finishing concrete are permanent mistakes. Depending on how important it is that the new concrete is flat and level, you should consider hiring a pro with lots of experience to get it flat and level for you.