Of course everybody progresses at a different rate, but for what it's worth, it took me 4 weeks to move out of the shallow end. That's 2 weeks doing basic drills, then 2 weeks working on breathing. Like you, I started at level 0. I was swimming 3 times a week for 45 minutes each session.
Looking back on it now, I shouldn't have been at all self-conscious about being mixed in with the little kids and shallow-water aerobics group. The pool is there for everybody. You have as much right to it as anybody.