QANTAS checking luggage through

It is 4+ hours in lounge! How much more do you need? And you have to change terminal anyway. So fail to see much of the problem. Though worth to ask anyway.

And out of curiosity - why the heck I would fly PER-SYD and then back if direct flight PER-DOH exist? Just to sit 5 hours in First Lounge? Seriously?

Strictly speaking, you won't be able to through check your bags but there is no harm asking. At least you have plenty of time to connect if QF PER cannot accommodate you.

I'm wondering if you're better off getting an Uber from SYD domestic to the International terminal, as opposed to the train?

Whatever rocking your boat. I would not sit additional 8 hours in the sky just to experience First. No freaking way - business is good enough for me. If you have curiosity then yes, I flown First.

I do not have any problem with yours or his approach. But for me flying First instead of Business is not enough incentive to make 8 hr detour and especially if it via Sydney where I avoiding domestic<->international transfer as a plague. Though I must admin that recent years it became only pain in the tail while before it was true and genuine pain in the a$$.

Main pain in the butt is of course international-domestic transfer when you have to pass passport control, collect baggage, clear customs and then before catching air-conditioned bus to other terminal RECHECK BLOODY BAGGAGE AGAIN!!!!! . When some poor fellow must do it because they live far away from international airports I cannot get why QF forcing me, a Melbourian (second biggest city in the country!) going through such nightmare. Again, now it became better organized and more civilized, but just few years ago it was true and genuine nightmare. One day I managed to miss my domestic flight because I arrived too late. No worries - good Australian Qantas put you on another flight without any fuss. However you have to stay looooong time in loooooong queue to re-check. And in the morning some miracles happens: "Passengers arrived from Los Angeles by flight XXX and heading to Adelaide by flight YYY please move forward". Then "Passenger arrived from Hong Kong by flight AAA and flying to Hobart by flight BBB please move forward". Then .... You got the picture. I missed my bloody flight and thus they WILL NEVER call me. I was standing like 10-th person in the queue for MORE THAN AN HOUR watching how all happier pax "moving forward". I finished it with huge loud scandal calling supervisor and vigorously expressed my disgust with f####g Sydney airport and frankly quite a few pax that been in pretty much the same situation supported me.
In Melbourne for example such things never happens - take your bags, go upstairs and check at corresponding counter.
Why I dislike Sydney international-domestic transfer? Perhaps simply because I am Melbourian? LOL!!!!!

It's an exception that Qantas allows, but other airlines may not.