Auto Pilot

Can be done from about 500ft AGL....depends when you want to let it take over really.

In real life it depends on who you fly for,as different airlines have different policies
As a rough guide most will engage A/P at about 2000ft,or once the aircraft is stable and flaps have been retracted

If I want it to be on auto pilot for the journey I usually engage at 1,000 AGL or when flaps are fully retracted.

I usually do it whenever I'm certain it won't make me smack into the side of the nearest mountain, if I have the wrong button pushed (like Heading instead of Nav). Not that I ever make dumb mistakes like that, of course.

Ed

Best thing to do to avoid the situation described above.
Flight director ON.
AP OFF AT arm
Dial in speed V2/V2+15, heading/Nav, altitude.
After departure the FD should give a sensible indication if it does then engage the AP. (500ft AGL minimum)
It depends on the AP you are using but my method:
As above having everything set on the ground on the AP ie step altitude, heading.... + rate verified & crosschecked then gear up. 500ft press heading and alt (speed) verify FD is correct sense then engage AP, at 1500ft dial in speed to 250kts retract flaps on speed schedule.
Very basic but gives good discipline for those who are serious with FS