Is it too soon to move or introduce another litter box for 6 1/2wk old kitten?

We found a 4 wk old kitten along the roadside. He's been here two weeks. He has a litter box inside a large dog cage located in our family room. We have two large dogs, and kept him in there at night and when not around to supervise for his safety. Things are going smoothly, so I leave him out of the cage during the day, but still put him in at night. The litter box needs to eventually be moved to the laundry room with a cat door that has been installed.(2 rooms away). So, the question is, can I try to start introducing him to another litter box in the laundry room? Is he too young to grasp having two litter boxes? Can I eliminate the other one? I can't gradually move it, because the dogs want to eat the cat poop. Or is it better to wait until he's a little older?