There are a few different quality establishments in which you can hire a quality fishing boat in Melbourne from. The great thing is, regardless as to where abouts you live in Melbourne; then chances are you won't have to travel very far in order to hire a suitable fishing boat for the day.
Bluey's Boat House at Mordialloc allows you to hire a boat for a minimum of two hours to a full day without the need for a boat license. Flexibility is offered should you choose to use the boat for longer than anticipated, however additional casual rates apply. You must be 18 years or over to be able to use these boats. Lifejackets are also provided. Swimming from the boat is not allowed, and alcohol can only be consumed sensibly. You are only allowed to travel two nautical miles (3kms) in any direction after you leave the marina. Advice on where to catch quality fish is provided, and even a novice fisher can still catch a decent amount of fish like yours truly has. Fishing licenses are available from this organisation at a minimum charge of $6 for two days. This is a state Government requirement.
If you wish to fish a little further out of Melbourne, then Fishing Boats For Hire is a great source to go to that also covers Port Phillip Bay. Quality boat hires are also available in Williamstown. Happy fishing.