Melbourne is an absolute treasure (I say without a hint of bias). But in May, I agree with choosing QLD (gasp) due to the weather.
Surfers though, is like Miami without the culture. It's a big, loud party town. The beach is nice don't get me wrong. But you can do better.
Perhaps fly to BNE or MCY, and spend some time on the Sunshine Coast instead. Noosa is nice. Or, an overlooked destination is Townsville and Magnetic Island. Personally I think for a tourist, Townsville/MI tick a huge amount of boxes for a cheap price, and it won't be packed with foreign tourists like Cairns or Surfers. (Nothing wrong with foreigners, I am one myself, but if you want an Australian experience it is nice to avoid places without any Aussies!)