It doesn't matter if the car has them now or not, what matters is what the relevant legislation says. In NSW that would be the "Motor Traffic Act 1909 [as ammended]"
The way I remember it here in NSW, in the late 60's or perhaps the very early 70's there was a law passed that made it mandatory for all cars first registered on & after the first of January 1965 to have front seat belts fitted, & thousands of cars were retro fitted with belts to allow them to be re-registered the next time round.
In practice, this law applied to all 1965 'models' regardless of actual date of manufacture.
I do not know if this was duplicated in other states.

Check with your relevant registration authaurities to be sure of the rules, although I think that you will be OK without them.
If you are going with a roll cage, & will not be carrying rear seat passengers, then perhaps removal of the seat, then fitting an alloy bulkhead cover to seal the cabin, & carpeting the whole floor/bulkhead area might be an option.

Any rear seat passengers really should have a seat belt.