i see (and answer) a lot of posts both here and elsewhere about 1kW inverters. my immediate answer is usually something along the lines of "there's no such thing as a free lunch". first of all do the math. 1000W/12V=83A. assuming about 15% in losses, that's pretty close to 100A. not only are we talking "heavy iron" here for a transformer, we're talking heavy copper too, since the wire used in the primary circuit needs to have negligible copper losses at 100A. you also need about 20 MOSFETs per side (of a split winding on the transformer) assuming 10A devices, and a safety factor of 2:1. that also makes for a very large heat sink. so basically we're looking for a "welding" transformer with a 12Vct @100A winding, 00ga wire (or at the very very least 2ga kept very very short) 40 MOSFETs, and a very big heat sink.
like i said above, there are 1000W inverters that can be had for free, but it takes a bit of looking to find one that works from 12V....