Need advice for using a mini split with a solar set up that I will be doing

Welcome to the forum @clabbin

That unit is very similar to the Diakin one I installed, the compressor is soft start so a 1.8Kw inverter should handle it without problems, 10Kw battery should be good but it really depends on other loads and the ability to recharge. If the opportunity exists to use grid power, or generator if need be, along a power logging device, to get an accurate consumption figure in actual conditions, that would be the best to aid design. The unit I use is for a 200 square foot insulated room, once the setpoint temperature, which uses 500W for ~15 minutes , is met, it cycles using ~175W, the break between cycles is ~20W,  haven't had the opportunity to run extensive logging  because it was not needed soon after installation. The PV calculation will be based largely on consumption and sized, like the battery to cover x number of days of autonomy.