An EA50 Pilot reported deviating from the charted departure and triggering a terrain alert when he relied on a new autopilot that he was not familiar with.

Narrative

Performing the departure procedure I failed to promptly make the [charted] turn; resulting in a terrain alert from the Controller. This was due to the fact that I attempted to use my autopilot to climb to the initial 1;700 FT altitude restriction. The autopilot was only recently upgraded on the airplane and I became confused as to the mode it was in. On the takeoff with this autopilot on this departure you have to first go into TOGA mode then transition to ALT CHNG mode to 1;700; then at the DME point reset the climb altitude to 4;000 and reinstate ALT CHNG; all while doing the takeoff cleanup and switching to [Departure]. Not really too difficult; except that I have not flown much recently and this was my first real IMC departure with the new autopilot. In the past; with this departure; I have hand flown the airplane at least until past the 1;700 FT restriction. The autopilot actually increased my workload due to my lack of familiarity. Corrective action is to fly more frequently; including going out with an instructor and practicing more.