There are two reasons you might need a larger service.

You might simply not have enough amps available. Your house is small, and
you have no big appliances, so that should not be a problem. Even if it is,
you can always do it later just as well when you start popping the main
breaker.

The other reason is that you might have excessive voltage drop to your panel
with the stove going. That might happen if you are a distance from the
transformer and they used smallish cables. You can test for that by turning
everything in the house on and testing voltage on both legs at the panel, or
at outlets on lightly used circuits. If you are reading more than a 4 volt
drop from when nothing in the house it running, you might have a problem.
Be sure to test both legs. If one is low and the other is okay, you might
be able to rearrange the loads (after installing the stove) to make both
legs okay.

I expect the fine folks here will come up with additional reason why you
need a new service. I can't wait to see what they are.