I have an educated hunch the US program of sharing a few nuclear weapons with some lucky Western European countries (and with Turkey) is a subject for discussion under AUKUS.
The Western European/Turkish nuclear delivery platforms are joint strike fighters (eg. F-16s increasingly F-35As) armed with "dial-a-yield" B61 nuclear free-fall bombs. "In case of war, the United States has told NATO allies the Non-Proliferation Treaty (NPT) would no longer be in effect".
Any sharing with Australia would need to involve much longer range delivery platforms eg. B-21 very long range bombers if sold to Australia (possible publicity 2023 as anti-shipping strike aircraft), possibly Aus and US developed ICBMs by (say) 2033, not to mention AUKUS SSNs that could be hypersonic cruise missile capable (2040s).
Regarding SSN platforms 4 vertically launched Long-Range Hypersonic Weapons (LRHWs) could be carried on each SSN. LRHWs may be deployed within the US Army and USN by the mid-late 2020s.
Back to Western Europe/Turkey regarding longer range delivery platforms :
"Historically, the shared nuclear weapon delivery systems were not restricted to bombs. Greece used Nike-Hercules Missiles....PGM-19 Jupiter medium-range ballistic missiles were shared with Italian air force units and Turkish units with U.S. dual key systems to enable the warheads.[9] PGM-17 Thor intermediate-range ballistic missiles were forward deployed to the UK with RAF crews."
The beauty of Aus/US ICBMs is that US personnel could be joint based. The location of a 100? silo missile area would ideally be in central Australia (to give longer launch on warning). If it had to be based south then the northern portion of the 122,188 km2 RAAF Woomera Range Complex might be acceptable. There could be a AUS-US dual key/code system to enable the warheads.
Also AUS-US dual key control on Aus B-21s and SSNs may be doable.
The above details courtesy RO-NW-WG.