Both are fine, natural, and could be said that way by a native speaker.
I personally (US native) would probably say "How many hours of sleep do you get?" I would not bother to say "at night" unless the context made it necessary. I think the reason I would say "get" is that sleep is something that people "need" and try to "get."
I personally would _answer_ the question by saying "I average six or seven hours a night, but I often take an afternoon nap as well."