Heathrow

1) If at all possible, do this on one ticket. Then:
a) The airline won't sell you the ticket unless there is in their opinion enough time.
b) You luggage gets checked through to Paris.
c) You stay airside (no immigration/passport control)
d) If you miss the second flight because your incoming flight is late, they will put you on the next flight to Paris.

2) Second choice, fly direct to Paris

3) If you absolutely insist on doing this. Be aware you will have to:
a) Go through immigration (passport control, 30-90 minutes).
b) Then pick up your bags.
c) Then change terminals T3, T4 and T5 are all in different side of the runways, and need a train to get between them (30 minutes+)
d) Check in again (hand in bags, 20 minutes?).
e) Back in through security (15 minutes?).
f) And how long before departure do you need to be at the gate?

And, how on time is the Qantas flight. How often is it 1 or 2 hours late?
If you miss your second flight, you have to buy a new ticket at walk-up price (ouch).

If I did this (which I wouldn't), I would go for the 09:00 flight.
Why not spend a day ion London, then get the Eurostar the following morning?

You can avoid British immigration if you travel with hand luggage only.

You can do the landside terminal change between 3 to 5 either by underground (contactless payment card needed but not charged) or from the Heathrow Express platforms. Transfer to 4 can only be done by the latter.

For 5 you need to present yourself at security 35 minutes before departure time otherwise you won't be able to enter

Why fly to London if you want to get to Paris? Most flights from Australia will require a transfer somewhere en route. You could fly through Dubai to Paris just as easily as to London, and save the cost and stretch of a London-Paris flight.
If, however, you want to visit both London and Paris, the best approach is to use a multi-destination search function to put together an itinerary covering both cities. You can commute easily with a Eurostar tunnel train (assuming the French strikes have abated.) To emphasize: The long-distance flights must be arranged through a multi-destination search. You can't patch them together yourself.

The 7:20 connection is impossible, so rule that one out straight away. Heathrow is a big, complicated airport. It takes 90 minutes, minimum, to transfer from Terminal 3 to Terminal 5. (That's the official minimum connection time as given here. But as it happens, I did exactly that transfer two weeks ago, and that time is accurate. It was 90 minutes of either walking full speed or waiting in queues, with no time to stop for anything, and we barely made our connecting flight.) And that's assuming that you don't have to reclaim and recheck luggage (either because the luggage is checked through or because you didn't check any to begin with). With luggage, on separate tickets, forget it.

The 9:00 connection is probably doable. Even so, it would be a lot more comfortable if you could get a flight another couple of hours later.

the previous poster - khbuzzard - doesn't specify if they already had their boarding passes. It would be essential, for me, to know that. There are other unknowns. Which gates you arrive at and leave from. Some gates are closer than others - with differences of 10-20 minutes to get to them. If the lines will be long or short.

Then there's the possibility of a delay in your arrival at LHR - there are so many reasons. Your flight to LHR could be delayed (I can think of 3 reasons immediately), you could be in a holding pattern over London, or sitting on the tarmac waiting for a gate to open, there could be a delay in offloading luggage, or worse lost luggage.

From your post, it sounds like you already have the Qantas tickets and you will have checked luggage. I'm risk-averse, so I would plan to spend a night and take Eurostar.

I assume you have a reason for wanting to make the same-day connection to Paris on a separate ticket, rather than doing any of the things the other posters are suggesting (putting everything on one ticket, flying directly to Paris via another city, or staying a full day in London before connecting).

And I don't think that's a crazy thing to do, as long as you allow yourself enough time to make the connection (i.e., definitely more than two hours). We did something similar at the beginning of our trip: Flew from the US to Heathrow on one ticket, arriving at around 10:30 AM, then flew from Heathrow to Italy on another ticket, departing around 3:30 PM. (It was much cheaper for us to do it this way than to put everything on one ticket.) For this connection, we had no checked luggage, no change of terminal, and we already had our onward boarding passes in hand, but we had so much extra time to make the connection that we could probably have added any of those extra steps and still been fine.

Of course, if our inbound flight had been delayed by hours and hours and we'd missed our connection, we would have been on our own, with no responsibility by the airline to rebook us on another flight. That's always a risk with separate tickets, but it was a small one for us, because most flights are not delayed by hours and hours. If ours had been, our backup plan would have been to get the train to Stansted or Luton, stay the night, and get a cheap last-minute Ryanair flight to our destination the next morning. That plan would have cost us a few hundred dollars (a last-minute flight from Heathrow would have cost much more) and a day of our vacation, but the slight risk of having to incur that cost was one we were willing to take.

In your case, there are lots of ways to get from London to Paris - by plane, train, coach, or otherwise - so if your Qantas flight is severely delayed and you miss your connection, you'll have many options.

It seems OP may be coming from Perth on the non-stop to London.

Booking a single ticket flight ( with one stop) to Paris looks to cost about AUS$ 100 more than the flight to London.

Adding the cost of the London-Paris flight and all the drama/danger of separate tickets, it appears it would be better to book a flight to Paris with a change somewhere other than London, as a single booking.

To answer the posed question of 'how much time to allow between flights' in London, my advice in nothing less than 4 hrs.

My $0.02 ( US)