Honestly? Buy an inverter. They're 100x cheaper than what it would take to make a proper, reliable circuit.
There's a lot wrong here for a "1200W" solution. For one, high power levels like this are never done with line-freq transformers. I'm not saying 1200W transformers don't exist, but they'd be like 15lbs+, and very expensive. It's done with high-freq switchers instead which are much much smaller, lighter, and far cheaper.
And there's a whole book of things to do in controlling something like this, saturation protection, controlling MOSFET gates with good synchronization, etc.