Hi Jean,
Yes, Rolleston Street runs west up the hill off Wallace Street in Mt Cook, and as far as I know Mt Cook Prison, located off The Terrace not too far away and within walking distance, was the only prison in Wellington at that time. It even held executions there.
I recall an article in the Dominion Post late last year describing its history.
I can't help you with 'office of Quarters', sorry.
Regards, riley