Gearing and kids' bikes has been on my mind lately. Our eldest has had a 16" for a while and I've noticed her struggling slightly on uphills. Lower gears are the way to go. It turns out that changing the sprocket on the coaster brake hubs that are on most kids' bikes is easy peasy. No special tools are needed, nor any particular skill (I'm living proof!), Sheldon Brown describes the process much better than me. The hardest part was finding a sprocket. I scavenged one, but they're cheap as chips on eBay or whatever. It works better, so she tells me, and she goes up hills a bit better, to my eye.
I put on a 19T sprocket, replacing an 18T. Not a massive difference, but I wasn't aiming for one. I'm debating doing the opposite for our son; he's undergeared, to my eye.
Rather predictably, bike racers get all bug-eyed about this stuff. The ones who race single-speed bikes (like trackies or BMX racers) do anyway. I reckon it's worth a look for casual cycling as well.