I wouldn't consider getting a rabbit if it's going to live indoors, it's not fair to the cat nor to the rabbit - the rabbit's a natural target for the cat.
Also,older cats generally (in my experience) don't like kittens who aren't related to them, they are far too energetic for an an older boy to put up with. Older cats do sleep a lot - my three are older than yours and they spend at least 80% of their time asleep. 11's an average age but not that old - but older cats do call in the night, our Rover does it all the time. Can he get out at night? - he's not moaning because he needs the loo?
Take advice from your vet and from the many petcare websites about moving your cat to a new house - you're advised to keep him shut in one room for a few days, with food, water and litter, until the house settles down and he gets used to new smells. Feliway's very good for calming a troubled cat, I wouldnt' be without it now. I certainly wouldn't entertain the idea of the rabbit, to me it's asking for trouble. An intruder and a new house, all in a matter of weeks....