Take all of this with a grain of salt, as I've not done it, and am only going on 2nd hand info/internet searches...
You can get a train (Melbourne to Geelong)/bus to Apollo bay and then the Twelve Apostles (termini of the walk) from Southern Cross (Spencer Street) station.
You don't need to book this bus to get on, so you can train/bus to the start of your walk at Apollo bay, finish at Twelve Apostles (near Port Campbell) and wait for the next bus heading back to the city, just pay (somehow, I haven't done it) when you board.
There appears to be a change at Apollo Bay, and in true Victorian public transport fashion, the connecting service will have left 15 minutes before you arrive.
Melbourne is marvelously woeful in public transport options from Airport to City, unlike Brisbane, due to vested interests, so you'll need to taxi or get a Sky Bus type transport.
Gas could be acquired at a Kmart, if the city store stocks it, or somewhere nearby like Paddy Palin.
(both are in Bourke Street according to Google, who never lies, but both are the wrong end of Bourke street for a 5 min stroll. Maybe Taxi to top end of Bourke Street, get gas, tram (free in city center) down to Southern Cross, then catch your train?)
https://www.vline.com.au/getattachment/ ... Ocean-Road)
https://www.kmart.com.au/store-detail/Melbourne+Cbd/https://www.paddypallin.com.au/store-locator/melbourne/https://www.paddypallin.com.au/equipmen ... e/gas.html