Hey there
@Tiggy ... wow what a huge trip you are going on.
So, when coming to Aus, its helpful to remember its a huge country, and therefore the weather will vary dramatically.
So yes, a cardi or light coat will be needed for April in Adelaide, but you will need light daytime layers for the NT as it will still be quite warm, although by April the nights will be cool'ish. April will be coming to the end of the wet season, so you may find it very wet. Light fabrics for the heat, but long sleeves and pants to cover your skin, because there will still be mozzies. And yes ..... sun protection, we after all, are the leading country for skin cancer.
Those same light layers will be useful in Cairns, as yes, it will be humid, quite likely all of Queensland, as you come down the coast. That being said, you are right, you may be in a lot of air-conditioning, and yes, we do tend to run those quite cold. As you come down the NSW coast, you may find it a slight bit cooler, especially if you go to any of the mountains areas. You won't need a padded, heavy jacket ..... but cardigans, long pants, shoes/socks rather than sandals ... you may find a little bit of need for those.
I would put together a good sized capsule wardrobe, of pants and tunics in linen blends, rayon dresses, perhaps a loose fit kimino jacket for over them, and then a light-med weight cardi.. Cotton blend scarves are great to do double duty as sun protection, and to wrap around the neck if it gets cool. Good walking shoes/socks, and sandals for the hot days, swimmer.
Going up through the centre will be quite sparse population wise, but coming down the Qld and NSW coasts, you will encounter lots of civilisation, and therefore just about every medium to large sized town will have an charity shop, that you will be able to pick something up, should the weather do something unexpected.
Have fun on your epic holiday. I am sure you will love it.