We have taken our daughter there twice, once at 14 months and the 2nd time at 19 months. They do have a children's menu, pretty much the same as all the other WDW restaurants-hamburger, chicken fingers, Mickey pasta, etc.
Also, we've seen other kids in there each time we've eaten there (both with our daughter and before she was born) so yours definitely won't be the only ones. My suggestion though, if you're worried about taking them there for whatever reason, would be to make an early reservation. We ate early both times with our daughter and we could count the number of tables occupied on 1 hand. Without her though we used to eat later, and Bistro was packed at that time. Of course, time of year might have something to do with that I'm sure.