Arrays are directional and may not suit your purpose if you want Gippsland and Melbourne.
The link I provided shows a lot of passive units (park it next to your radio but no physical connection) which are portable.
Log periodics are nice but size would be a problem and ground plane could be a massive problem (we built a short wave log periodic in NW Australia in the 60's and dumped 20 tonnes of copper pellets in concrete to create an effective ground plane, the antenna was about 80' long and rotating), put one of those up and we would all know where you live.
Actually, if you know Bill Conolly in your part of town (Scooter) he might help you.
His house is covered in antennas which is a bit of a giveaway.