That usually depends on your airplane. I know it can be done in a C152 in 700 feet. I believe a DA 20 or 40 could do about the same, but I've never had a reason to try (pattern stays busy). I would never attempt that turn in an Arrow or Cherokee since the glide ratios aren't in your favor. It also depends on what you are capable of doing.

I used to set a specific altitude agreed upon between me and my student. There are so many factors that go into such as wind, aircraft, temperature, etc. If it was a straight out departure, then usually TPA was the minimum for us, but it all depends on your capabilities as well.