When I brought Jazz home at 14 weeks I had to keep her in my guest room for over three weeks because it turned out she had a URI (kitty cold) and ringworm so I had to keep her quarantined from Ripley. When we did finally start introducing her and letting her out it was no trouble to move her litterbox into the laundry room. Same with Scout when we did that with her after keeping her in the guest room for about a week. I don't think that will be any concern for you as long as you show the kitten where the box is in the laundry room.

I almost forgot. Welcome to PT!! I have three cats and a dog as you can see in my signature below. I look forward to meeting your furbaby. I think you cat will probably be happy to have the company, just take it slow.