One comment:

Assuming you aren't riding off-road, try to swap out knobby tires for slicks. This can make it much easier for your child (or, really anyone) to go faster and farther. Front suspension is another place where it can suck energy without providing much real gain.

For your original question: a mile and a half is well within most 6 year olds (depending on terrain). Another option is a trail-a-bike for longer rides. There are those here who use these to get their children to school (where you can either lock up the trail-a-bike at the school or just ride around with it laughing at the "hey, did you know your kid fell off?"comments).

Good luck and have fun!

Charles