You do Immigration and customs at MEL. Firstly you do Passport control then collect your luggage and go through Customs inspection. You then leave your bags for onward carriage to HBA.

Fortunately it is easy to connect between International and Domestic in MEL as it is within the one building complex.

All MEL-HBA flights are Australaian domestic - ie there is no facility to do International Customs in Hobart - but there is an agricultural dog sniffing inspection (ie a sniffer dog) checking for fruit and possibly other substances (but everyone is subject to that).

Notwithstanding, HBA does call itself an International Airport - but probably it has a long memory to when it did have flights direct to NZ.