This is purely speculation (for another day or two), but there should be plenty of options in the Kodak EasyShare line.
I haven't used it yet, but I picked up a Kodak C-330 from Microcenter for my daughter's 5th birthday (she turns 5 on Sunday - the day we arrive at WDW).
It is pretty small (definitely pocketable), 4MP, 3x Zoom (I think) and very inexpensive. (Looks like it is about $99 where you can find it).
I got it on a price mistake from Microcenter - $59 for the bundle with the camera AND the printer/dock.
I've always used olympus and canon digicams, but I've read in recent years that Kodak is doing very well for inexpensive cameras that both are easy to use and have decent picture quality.
Ted