Much of it is maintenance/protection from it getting too hot in the first place. So block sun wherever you can. You actually want to seal all of the openings to the house to keep the hot air OUT - which feels totally counterproductive but it does help. If you don't have heavy blinds or shutters, you can wrap cardboard in cooking foil and put them in the windows, that helps a bit.
Get an indoor/outdoor thermometer which will compare the two temperatures - can get pretty cheaply on amazon. In the abscence of this, obsessively check the current weather forecast to contrast with a thermometer you have indoors. As soon as it's colder outside, then you can fling open doors and windows to try and get the air moving, but once it's hotter outside, then you want to try and preserve that bubble of cooler air. Keep internal doors closed, too, as some rooms will be hotter than others.
From having had an air con which is really too small for the space - you need to get the air con on early in the morning before it heats up too much. Remember that air con works by removing heat as well as adding cool air, so if you're starting with a hotter room, it's going to have to work so much harder than if you start when it's comfortable and it's merely maintaining that temperature. It's also worth leaving it on if you're leaving the house for an hour or two or less, as it's less efficient to make it start again on a house which has had chance to heat up. But don't leave it on if you're out for longer because it's too expensive and not worth it. And don't run ANYTHING in the house which creates heat unless you have to, not even a laptop!
Getting out of the house does help, especially if you can go to big businesses which have proper, effective air con! Be careful of the sun in Australia, of course, but if you're sun safe the temperature will typically be around three degrees lower when you're near water, which can help bring it down to "more bearable" and actually getting into the water also obviously helps. Shade from trees is more effective than shade from thin man made materials, and shade from solid concrete or stone is much better than shade from wooden or plastic constructions. Tarmac often absorbs heat and makes you feel hotter when standing on it.
Take tissues or a thin scarf with you everywhere as you will sweat loads. Have cool baths and showers, several times a day if you want - 31 degrees is about right. Don't try to do anything non essential. Move slowly. Freeze your drinks - cold drinks are better than warm. Expect to snap at each other. It does get better - you get used to it but the first year (and I haven't even lived in Aus, just somewhere hotter than the UK) you will find it difficult. You also NEED to break the heat up by going to proper air conditioned places even if you just hang around the freezer section in the supermarket - several days in a row with no escape from the heat is a special kind of torture. Sometimes I go and sit in the basement with the spiders, which might be less fun in Australia!