How long would it take to sail a 50-foot yacht from Perth to Brisbane?

A long time. Much longer if you go the long way or if the wind doesn't blow.
Seriously, this isn't a question that can be answered with any accuracy. Too many variables.

How long have you got? Are you looking for a quick delivery ie you're Brisbane based and you've found a yacht in Perth.
I went the other way (Brisbane to Perth) taking 6 months. Another forum member did the same trip in 3 months. It can be done in less time, or it could take longer.

Been done in less than a month on my 40' boat. Fremantle to Rivergate.

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Andrew68 said..
Been done in less than a month on my 40' boat. Fremantle to Rivergate.

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Whats the name of your new boat Andrew? I'm pretty sure she has been in my neck of the woods a couple of years ago.