Around Shoalwater you would be surfing around the beach breaks at Secret Harbour, Surf Beach, Mandurah,...
Patience is the key and look for where there is a rip taking water back out through the sand banks. That should get you out fairly quickly, provided you wait for the lull between sets and not fight it too hard. If you come off your board, get back to shore and start again.
Since getting a narrower board, if it all looks like going a bit pear shaped I lie down and prone paddle back out, with the SUP paddle flat on the deck under my arm. Seems to work quite well.
Agreed with Gorgo that you look for a spot further up the beach and then paddle down to where you want to go. Just watch out for those nasty short and long boarders when you get there.