Luka,
ASWA used to use a site near Serpentine for some viewing. I think there's an oval there. I would think your best chance is to head in that direction, considering where you live. I wouldn't recommend setting up ON the oval this time of year as you may get sprinklers, but there may be somewhere in Serpentine, perhaps even a car park near the oval, that you could use.
To be honest Fremantle is a long way from dark skies, seeing as you're stuck with heading either 1 hour north/north-east to get barely to the north-eastern edge of the city or 1 hour east to again only get barely to the eastern edge of the city. 1 hour south and you're still in coastal development I guess? Hmm.
Edit: Jarrahdale might be another area where there's an oval or clear area somewhere near but not in centre of town, similar distance to Serpentine.
Roger.