You have said you are going down under for a month which is a fair old time, but visiting family makes it a bit easier. I am a demon light packer so here are my tips in general:
Minimise shoes. I used to go for a fortnight UK beach holiday with three pairs - walking boots, flip flops and trainers - and I only took the trainers bc I run. There is no Pembrokeshire family bucket and spade holiday occasion which cannot be answered by flip flops or walking boots. Even for a month in Aus I would only add maybe one pair of nice comfortable shoes - maybe Converse or similar - to wear to go out.
If you will have access to a washer (surely you will) you can halve the items. One hoody or one cardigan or whatever you wear like that. Wear your coat if taking one. Probs no need for Australia just now tho.
Take things that all go together - a dress that can go over a T shirt or be worn alone, trousers to go with the same T shirt, shorts ditto. That's four outfits from four items. Stick to black, white and one other colour.
Make up and toiletries - I use a lot of these (I mean a big variety) but when travelling I force myself to be minimal; one moisturiser for day and night, one serum ditto, one eyeshadow, one lipstick, small shampoo and toothpaste, hotel shower gel is fine. Samples of perfume are good.
Essentials - meds, underwear (but take less and wash if going for a month), passport, phone, charger, contact lenses, glasses.
I would never take hairdryer or all that even for a month. Surely you will be able to borrow one? Agree with PP - why two sets of gym kit? I went to Vienna for five says with DD, ran every day, just wore the same kit. It was fine. Well, the top was a bit yucky in the end but if I was really worried I could have washed and dried it in the hotel room.
Bear in mind that I will avoid checking in luggage if at all possible as the last time I did, it went missing and turned up three days later. Obv (I suppose) if I were going to Australia for a month, I would check in. But I recently flew on a three-day trip where I had to take three separate outfits apart from my actual clothes, plus shoes for those outfits, and my laptop, and still got it all in my carryon with ease.