This gives rise to another question though - can your inverter supply the surge that the motor startup will require. That depends entirely on its specs and of course the rating of the motor in the washing machine in the first place!!
If your inverter is really limited to 1000watts then the fuse should be spec'ed to suit it i.e. 1000 / 12 = 83.3 amps. Rounding up to the nearest likely value (since a fuse should be protecting only a fault condition) then you should be good to go with 100amp fuse. Robin - Down Under (or are you Up Over)