I think the NG has a limitation (or course company SOPs vary) of 400' after takeoff (think this is the boeing certification limit as opposed to company limit).
Most people hand fly for a bit after takeoff - certainly most cases well beyond flaps up - if things not to busy up to maybe 15000'.
A/P put in early with low altitude clearances after takeoff - so with the 737's piss weak A/P - we try to put it in at least 1000' before level off.
Of course with traffic, WX etc - common sense may suggest putting the autopilot in sooner rather than later.
Additionally, when we do RNP departures - we are required to put the Autopilot in (no later than) when we call for climb thrust (n1) usually this will be 1000'. Sometimes it is easier with these departures to put the A/P in at 400' - although the company has some conflicting information about that.
Anyway now that I have blabbed on about that - I see your pretty much referring to the 733 only. IN which case 1000' seems to be the min certified level.