Weather in Oct-Dec. Please dont say it will rain!

Technically Australia is still in a drought, although the last few weeks we've had floods in NSW and Vic.
Not a bad thing because most dams were between empty and 30% full.

As for the weather i'd do central Australia first as it will be warmer in October than southern Australia which is still a bit cold but gets warmer the closer to christmas.

There's no guarantees.
Usually in Melbourne, and most of the south east, its warming up in October and November but not really hot. There can be exceptions. It can also rain a fair bit in spring - Sydney gets four seasons in one day, Melbourne gets four seasons twice over in one hour. Tasmania is still cold, a Tas spring is sort of like a UK summer; occasionally it will hit 20 degrees.
By mid-late December, Melbourne starts getting strings of high 30s and maybe low 40s (always low 40s in late Jan, during the second week of the tennis), punctuated with wet days of 18 or 19. And by then the north goes into the wet season.
So, as other have said, if sticking to the east coast start in Cairns and work south. There are no guarantees it will be warm and dry, but its more likely than it is in the UK.

Always wanted to go to australia so if south america is going to be like london

I can't see any possible connection there old son. Come to Bahia, even when it rains ( and it won't be from Oct thru Dec) it's warm. Rain in Melbourne is akin to a cold shower ( when and if it rains, although according to friends there it's been pissing down of late).

Well, as you can see from all the answers, it could be quite variable and no guarantees on that either.
About the only definite is as #8 says, do the north and Uluru first, for it will be hotter and possibly wetter in Darwin come December than it will be for October, but already getting warm - never much below 30C in Darwin most anytime.
Usually a great day for Melbourne Cup, first Tuesday in November, not to be missed come rain, hail, snow or dust storm and any could occur whilst the beer still flows.