We came over with 4 Staffordshire Bull Terriers aged from 2 years to 13 years.
The oldest girl was 13.5 years at the time, she's now 15. There was never an option of leaving her behind, she was healthy, a very good traveller etc.
The dogs all cope with the heat very well, tbh just like us when you arrive you think 25 is hot but within a year you are wearing a cardigan at them temps. Added to this in the height of Summer they mostly just want to lounge in the house with air con on anyway and there are the colder months for them to enjoy as well in Brissy.
If you have a good vet you can trust then have a chat to them about how the flight will disrupt any medications Patamon may be on for his cushings if this is a concern.
We were renting near Brissy when we had our dogs in quarantine at Sydney and although many fly their dogs up to Qld we drove down, stayed with friends overnight and then picked them up at 8.30am and set off back for the rental took about 11 hours but well worth it in our instance.
It was never the quarantine that worried me but the flight itself, the flight to Sydney for dogs is the quickest with just an hour stop in Bangkok (they don't get off the plane, same plane goes onwards). The staff at quarantine were brilliant you get the mobile number for the kennel-hand that is looking after your dogs and she always knew when we rang and launched into weights, how they were doing etc. I hadn't told them that our old girl had gone deaf in case there was some obscure rule about them not flying LOL but they knew on the first call to them that she couldn't hear (it wasn't and isn't a problem). When we visited them after a week, they were very healthy and happy it was nice to see them all run to the door, tails wagging when the kennel maid went past.
Ours were there in April and we had a good spot, last kennel block down so it was lovely and shady. I would imagine in summer they use the blockout shade material which is very good. By it's very nature it's quarantine so the dogs have to be monitored very closely, so I wouldn't worry unduly about his time there.
We did leave behind with my very good friend our old boy who was approaching 16 years old, we could have brought him but his back legs weren't good and he'd always been a very bad traveller. I guess it's really only you that truly knows Patamon and what you think will be best for him.
I used to work in rescue for my breed and oldies are generally easy to home and there are some super homes out there, but if you can take him if it's right for him, I suspect as the previous poster says the short term stress will be quickly forgotten to be with his family.
Good luck with your move and with whatever you decide