Labour Day isn't a particularly big event in Melbourne, most people just do their own thing - ie, take the opportunity to have bigger nights over the weekend and have the Monday to recover.
There is one major civic event on that day: the Moomba festival, which is a carnival and cultural festival, and the Moomba parade on Labour day morning. This is mostly attended by families with young kids.
For music-loving young adults, there's the Golden Plains festival at Meredith, about 2 hours' drive from Melbourne, which runs from the Saturday before for 2 nights, ending on Labour Day morning.
Aside from that, most of the shops, restaurants, bars and pubs are open, and this time of year has the most reliably pleasant weather so it can be a great day for a picnic or a daytrip to the hills, the coast or the wine country. about 8 years ago