Like SammyC said, you have to be able to make an argument for value versus the immense cost. This discussion has been had time and time again, but it is an interesting one.
Most tend to focus the conversation on fighters, but, for me, when HMAS Melbourne was retired without replacement, I think the greatest loss was the ASW capability. With more MH-60Rs, and the goal of a larger surface fleet, that situation is being improved, and that begs the question as to whether we would need a "dedicated" ship. e.g. If you had a (future) task force of, say, a Hobart, two Hunters / interim frigates, and an LHD, you would likely have six Romeos afloat and with two sorties a day each, they could certainly maintain one in the air at all times on ASW patrol. This is without considering too what role drones could play in ASW in the future.
The other question that is often raised is even with embarked F-35Bs, what do they do for you? Go back to Todjaeger's post, where he talks about eight aircraft flying three sorties a day - 24 in total. Ok, could be useful. But what about maintaining a CAP? I believe you'd need about eight to ten sorties a day to keep one aircraft airborne. Doesn't leave you with much does it? Without a CAP, you're more vulnerable; with one you can't send out as many strike sorties. Then, as Sammy said, you start to do the maths on using F-35As with tanker support.
To confer useful capabilities, I'd suggest the "dedicated" ship would need to be akin to the Cavour, which is currently visiting Australia, at the minimum. But how do we afford that, and nuclear submarines and everything else, and where do we get the crew from? And is it worth it, all things considered?