[Shaun_MD]

I figured for a 750watt pump, 2x that for surge would be about 1500 watts. I need a bigger inverter?

[MrB]

You need a smaller pump. A backup pump with low flow pumping into an elevated tank for pressure and on demand water.

Your pump currently is sized to provide your water on demand.
Can’t do that on a battery.

[Bobalu]

You may, best way to find out is charge the battery and hook up the invertor to the pump and see if it will start.

[PA Engineer]

I figured for a 750watt pump, 2x that for surge would be about 1500 watts. I need a bigger inverter

You need to find out what the locked rotor code is for your pump. An explanation of this is here.

My pump is 3/4HP and draws a nominal 1,920 watts, however the code for the pump is G. The measured inrush to start it is around 9000 watts.

Think of it like a garden hose. When you turn the hose on, no water comes out until it fills up.

You will probably need a higher output invertor. Also, try to buy one that is pure sine wave. The output will need to handle two "inrush" loads. Your refrigerator will also require a higher starting output.

Finally, you will need to get a simple watt hour meter to calculate your loads.

Hope this helps you begin, because you will need to know your max loads and total watthours used before designing.