WA does recognise your interstate licence, but not your firearm registrations.
Your firearms are considered "unregistered" as soon as you cross the border with them, that's why you need a temporary permit for them. You can take the permit out for three months, and can renew it _once_, so you can stretch it to six-months max. Costs about $54 a month. Be sure that they also list ammunition on the permit or it is an offence to possess ammo (or empty brass) for the firearms despite the permit to possess them.
If you are moving there to live you can get a free two-week permit to allow you to transport them to a dealer who will keep them (for a fee) until you have your WA licence.
If you want to use your firearms anywhere other than approved ranges you will need a property owner's letter.
Overall, it would probably be cheaper to leave them with a friend until you have your WA licence, then have a dealer send them over to you.
Does anybody know if you still have to pay the exorbitant WA compliance fee on firearms you already own?