What Does an Average Joe Actually Have to Use?
A truly Average Joe does not have the money you described ($1,000,000 AUD); they have much less available, particularly at the start of things. They may be able to get a few thousand dollars together without much hassle, but it may actually be too little to even invest. So they would necessarily need to turn to ventures which accept little money and which can, with some foresight, provide significant returns.
Option A - The Lottery (But we can't do that)
You have already ruled out the lottery, though it is the real first answer. I agree it is probably a more common plot for this kind of thing, but there's a reason for that - it's what everyone would do. The current PowerBall lottery payout in the USA is more than 200,000,000 right now, and for $2 it could be Joe's. Picturing another option seems difficult in comparison, but I suppose we can try something.
Option B - Gambling
I think this is a fun area for a plot, because it has so many major flaws that your Average Joe wouldn't be thinking about. If you know the outcome, gambling in a casino is a great way to multiply money quickly, which you could then use to fund other ventures. There are some major complications though. Such as:
- Let's say the character remembers the first 5 places a roulette wheel will land on after 11am - 12, 17, 8, 24, 1. They come up to the table with a thousand dollars in chips and put them all on #12 confidently. But the number 15 comes up instead. Why? Because the people monitoring the table took an extra few seconds to make sure the time traveler's pile was properly set up, affecting the ball spin.
- Games like Craps would similarly be affected. As would card games, assuming that the position "Joe" takes would otherwise have been vacant (dealing cards out faster).
- Slot machines are based on random variables, and just because a machine payed out when a player pulled the lever at 12:01:12pm does not mean it would if Joe did (because the first player pulled eat at 12:01:12.001 and Joe pulled it at 12:01:12.052, and microsecond time is probably used as a randomization component).
- When Joe finally did find a game that worked for a time traveller, the Casino would assume the game is rigged and shut it down pretty quickly.
- Oh, and once Joe has been kicked out of another casino after a streak of luck that defies odds, he would probably be blacklisted from all other casinos in the area and be invited to the police station for a chat. He wouldn't ultimately be charged with anything, but still questioned.
- Even things like horse racing - where Joe wouldn't seem to be able to affect the outcome - aren't immune. Once a jockey hears that someone has dropped a HUGE pile of money on the outcome of their race (and they would though word of mouth) they may become nervous and end up losing their concentration and the race.
Option C - Take it Slow
After the fiasco with "get rich quick" schemes (what was described above and many others), "Joe" realizes something - he has all the time in the world. Once you can restart days and you can't seem to die, time itself takes on a very different meaning. You don't really need a trillion dollars now - all you need is what you can spend, and you have all the time in the world to get more. So "Joe" can take the bit of money he has built up through the get-rich-quick schemes and put it into the stock market only when something big happens. It won't be every day, but it doesn't need to be. Even if Joe invests only 4-5 times in a year, he can still comfortably make more than he can spend. All without having to go back in time repeatedly for a bunch of smaller gains.
An agency similar to the SEC would undoubtedly investigate "Joe" and he would be audited yearly, but provided that he continues not to hobnob with company executives he should be fine. To keep things really clean he could continue to live in Australia and only invest in companies that keep all of their operations in England, France, the United States, or Canada. Taking out subscriptions to local papers and magazines in all those countries (which he would, of course, discard unread) would also help spread the idea that he is just plain smarter about the stock market than everyone else.