Having only a hammock and no sleeping bag, that's really limiting. You can get some 4 person tents for not much at Big W or K-Mart. They're rubbish, but if you don't want to invest in a big 600 $ tent because it's only gonna be for this time then it'll do the job.
Now you need to tell us when you intend to do this trip. Obviously you can't go to the Alpine area right now because you'd have to pay some fees to enter the resorts, many roads are still closed, and there's snow in the summits, not ideal for a beginner.
September would be a great month to enjoy the Mallee country. There is a 3 day walk in Murray Sunset national park, in semi-arid country. Plenty ,of kangaroos, emus etc..., magnificent pink lakes, and it's easy going as it's completely flat. You can also try the Little Desert discovery walk, here :
http://www.visitvictoria.com/Regions/Gr ... -Walk.aspx . Early spring is good for orchids/wildflowers if it has rained enough. Problem : it's pretty far from Melbourne. Little Desert is 4h30, Murray Sunset more like 5h30.
Now for coastal walking there are plenty of options. Croajingolong is, I reckon, the best one : it's wild, it's biodiverse, you won't see a soul most of the time. You could try and contact this fellow :
viewtopic.php?f=37&t=14740 , because it's a one way walk so you need to arrange a pickup or dropoff. A classic of coastal walking is the South of Wilsons Promontory, several topics are open in this forum on the subject, and have a look here :
http://parkweb.vic.gov.au/__data/assets ... -Hikes.pdf you can do 2, 3 or 4 nights. It's easy navigation most of the time (the Northern circuit isn't), and it's close to Melbourne (2h30). But you certainly won't be alone, it's a popular destination (well, it still only means seeing a max of 10 people a day).
As for options in the Alpine NP I've only been there a couple of times and never did an overnight hike there, so I'll let the others fill you in. The Grampians would be obviously nice too, still close to Melbourne (3h) but I don't know of any 4 day hike, the main ones like Mitchell Plateau and The Fortress are 2 nights, some guys on the forum have done longer, but involving quite a bit of off-track sections.
The last option would be Lerderderg gorge yes, but for your first overnight hike, there's better to do. Lerderderg is nice because it's very close to Melbourne, but it's not the best scenery in the state, it's nowhere near the magnificence of Croajingolong, the Prom, the Grampians or the Alps.