First, the HP rating of a motor is the output power, not the input electrical demands. Does this plug into a normal 120V socket? 1.5HP is 20amps full load current (10amps for 240V) according to the national electrical code. I have my doubts the motor is REALLY 1.5HP, since a lot of marketing of motor products list some kind of "maximum" HP, which you would never sustain in real life because the motor would stall. If you can find a current (amps) rating for the compressor, that would be the thing to use.
Next, it will draw more current during startup, and the inverter needs to handle that. If it lists a stalled rotor current or similar on the nameplate you could use that. The national electrical code would allow an instantaneous trip circuit breaker of 8 times the full load current for a motor. My point is the inverter size will be significantly larger than the running amps of the motor would indicate. The 1200W inverter you mention can supply 10amps at 120V. That won't cut it for a 1.5HP motor, but like I said, you may not really have a motor that big.