I've taken my empty stove with me serveral times, and have not had problems when it is EMPTY in the checked baggage. This includes when I took it on a SFO-LAX-NAN-AKL trip on UA/NZ.

You should be fine. Just really make sure it is empty (I usually have to burn off the excess fuel). The canister might be a bit more of a challenge, but camping stoves are NOT prohibited items.

Enjoy your relocation!