I'd also recommend avoiding Terriers ours is 'good' around small furries but I wouldn't trust her 100% as if they move quickly she does twitch!
Our lab on the other hand is lovely and would tick your boxes! We have spent alot of time training her!!
I moved my dog downstairs when we moved into our first house. Would babygate the top of the stairs then start by moving his bed onto the landing for a couple of days or until settled then slowly move away.
Then to bottom of stairs (gate the bottom) and finally to where you'd like the bed to be.