KC130 and kc30 can refuel F-35B.
I'm not sure basing all the refuelling assets on a small carrier is ideal. You are then operating another type of aircraft, needing to launch and recover it, etc. Draining already limited capability. More deck, more hangar, more crew, more fuel etc.
In Australia's case, I would see E7/P8 and KC130 operating along side a carrier, possibly with MC-55A. While not organic to the task force, these are long ranged aircraft, able to loiter for ~8-16 hrs at a time at range, and can be crewed with multiple pilots and refuelled in the air. While not organic with the fleet, I struggle to see where we would need to provide full spectrum capability more than ~10000km from a friendly airbase, by ourselves. We have enough of these platforms to maintain a continuous rotation of aircraft indefinitely. These platforms could operate from mainland Australia or remote bases like Christmas Island or Norfolk Island etc. If operating from Butterworth, coverage all up through Asia north Indian ocean etc.
Its the fighters that are short ranged, and require a massive logistics focus to sustain any sort of air presence. Requiring squadrons for individual unit providing reliable coverage. While heavy strike packages could be arranged to come in from proper land bases, its the presence part of the calculation that is very difficult to do, particularly in a defensive role.
As an organic flight, of say 6-8 aircraft, they could be armed with say ~4x spear3 each in a stealth configuration (24-32 missiles). With a range of ~150-200km beyond the max flight range, does give a pretty long armed strike range with reasonable saturation for an organic force, and can rearm and strike basically continuously able to deplete even a large ship defensive missile loadout fairly quickly. With minimal compromises in low observables JSM or other heavier/longer range weapons could be added. If the war is depleting stocks of missiles, guided gravity weapons still offer formidable standoff well away from the fleet. From ~2028.
The advantage of a carrier is there is less pressure on building larger and larger surface combatants with larger and larger missile loadouts. Even with long range munitions, in grey situations, presence and manned platforms are everything. In theory a P8 shouldn't be flying within visual range of a opposing fighter, but currently in grey operations, fighters are dumping chaff into P8 engines.
If there is no big war, but a continued and extended grey regional competition, then having great organic presence in the region is likely to be a huge advantage.
Where I guess the value of a carrier is if that sort of threat and capability is something the ADF sees in our region and where we want to operate. While the US has great carrier power, it isn't often seen locally down with our region, and it is easily monopolized and prioritized elsewhere.