I don't know about your child but most young kids don't have the greatest attention span. Not saying yours doesn't, just my experience. That said I'd keep it close to home. Not that a good road trip isn't fun but I know I hated road trips when I was young. I'd keep it short and sweet and try to catch a bunch of them. Georgetown would be a good bet and it's the closest of the ones you mentioned. It's still about 2 hours from Bozeman and it can be COLD up there but you can just about expect to catch something. My self personally, the EGRA is a great place for kids and tons of fish to keep them busy, really close. The pond by the mall you can catch 20 fish in an hour. Same with the ponds off Oak. Canyon Ferry can be really good for trout and they are pretty good size and not to far. Causeway as well, you can catch quite a few trout there and not much farther than CF
A young kid will have a bunch of fun no matter what as long as they are occupied, just my .02
