Melbourne is known for its snapper season for those "big reds" from September to March of any given calendar year; and Port Phillip Bay is the best locale to go deep sea fishing, and Reel Time Fishing Charters have a bit of a reputation for ensuring that their guests take home some quality fish, regardless of age and gender; they promise a fun day to be enjoyed by all. The meeting point is usually at Carrum, however if you are wanting to find out more; you should check this out in advance.
Otherwise, for something a little closer to the city, the St Kilda Charters also offers quality deep sea fishing with reels and refreshments provided; yet it is still advisable to bring your own lunch, and this provider provides a slightly larger boat called the West Wind. Numbers are capped at 30 people.
Great to go out and enjoy in groups. The best way to go deep sea fishing, and common sense is a must. Regardless of the weather (and its appropriate too, because summer is generally deep sea fishing season) remember to put on some sunscreen prior to and during the experience as much as possible.
And even if you say that "I do not get seasick" remember to always come prepared, and in the seas (and depending on the type of boat travelled in) remember to ensure you have some seasick tablets at hand. Travacalm is the preferred brand - the original flavour, and do not go for any seasick tablets with ginger or other natural remedies; that's right you know what will happen and it won't be pleasant. Also it is a good idea to come prepared with a few acupressure bands in case seasickness comes in.
Best to dress in bike pants and a t-shirt, and remember to pack some cooler clothes just in case, and most importantly while deep sea fishing (also from experience) it is wise to drink plenty of water and stay hydrated. Eat sparingly if you have to, and remember to catch plenty of quality fish.