@pingc383 I travel with fsh and gh back and forth between Melbourne and Brisbane, just make sure you put 2 packs of ice in the insulation bag and store in your checkin luggage, it should be fine. Normally ice is still rock hard when I unpack it.
Also the girls from the clinic might be able to organise a courier to send the gh down to you, it was offered to me as an option but I managed to find it locally for $365 per vial/10mg. Have you checked with pharmacy partnered with ivf clinic locally? I normally need 3 to 4 vials per cycle.