First up, GOOD ON YOU for being so organised and thinking about it now! I field at least four or five calls a day in our centre from parents wanting to get their 20 month old in NOW...
Lady Gowrie is an incredibly lovely centre, but you might not get the baby in by the time it's one, even if you have your name down now.
ECMS run a centre next to St Vincents, I think, I haven't been since before it opened, but it ticks all the boxes I need to for a good centre.
City of Melbourne also owns four good centres, two of them in Carlton. John So ran them into the ground a bit, but they're still of good standard.
Kids on Collins and Sunkids, both at the Spencer St end of Collins St are available, but both are for-profit, and therefore, in my book, not an option.
Moonee Valley City Council also has a centre in North Melbourne that is great. I was offered a job there and one of my biggest regrets is not taking it.
Ummmm.... I'm sure there's more, but I can't think of them from up here right now. There are also loads and loads of great centres in the suburbs, most easier to get a place at than the city centres. Another thing to consider is, do you really want to face the trip home with an exhausted and grotty child? So depending on where you live, I can recommend more places.