4 years is way young. I think 6 is the very earliest age and that is young. Its like herding cats, a room full of little kids. Hope you have another adult or two to help. You'll need them.
I teach starting at 4, they can do quite well. It's not easy though, and requires a whole different approach to teaching then older kids.
Lots of combat games, and switching gears every few minutes.
Anyways, as for the question. I rank kids white to black, taking around 5 years to get to black for a kid starting at 7 or 8, a little longer if they start younger. Of course my situation is different, I don't rank adults. So they get their black shortly before they'd be moving into the adult classes and going "beltless".
However, personally if I was ranking adults it wouldn't change for the kids. The Kids program goes white to black, they have their own curriculum and a checklist of requirements at each level.
For kids belts can be a pretty big motivator, and if they look around and see friends getting black belts in karate or TKD and they get told they aren't allowed to get even a blue belt until they are 16 its going to discourage them.
The Kid-based styles have a long history of ranking kids and figuring out what works and what doesn't in terms of retention and motivating kids, IMO its worth paying attention to what they have learnt and not trying to force a adult system into a kids class.
It's a idea not without precedent, not sure how things work in the states, but up here we have cadets, basically a military like thing for kids, run by the military. They have their own uniforms and their own rank. A 13 year old can be a Sargent, but if when they turn 17 they enlist the rank obviously doesn't carryover.