Clunking sound when doing a quick start with 2005 Cadillac SRX

When I make a quick start I get a clunk kind of sound that appears to be from the area near the transmission shift lever on the console between the seats. If I really do a jack rabbit start, it will clunk repeatedly until I let up on the gas or the car gets up to speed.

Is this a broken Engine or Transmission mount?

Based on the symptoms, broken mounts are a very strong possibility.
I would suggest avoiding those jackrabbit starts at least until the mounts have been checked and replaced if necessary.

While it is up on the lift, have your mechanic check both the u-joints and the splined shaft of the driveshaft.