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Using WebJet travel for looking at return flights between Sydney and Brisbane, I noticed that even when I looked as far ahead as possible (Saturday 16 September to Sunday 17 September, approximately 11 months in the future), the cheapest flight from Brisbane back to Sydney was a Virgin Australia flight at 7 AM at $99, approximately $50 cheaper than other Virgin Australia "Getaway" return flights from Brisbane to Sydney.

Is this because some tickets have already been sold for other times in the day, driving those prices up, or do airlines have a lower initial price for some slots compared to others?

I had a brief look at How do airlines determine ticket prices? but it didn't seem to answer this.

do airlines have a lower initial price for some slots compared to others?

Yes. It is unlikely to be just coincidence that the cheapest you found was an 07:00 departure. 45 minutes is recommended for bag drop off, so arrival should be by 06:15 - say 06:00 to allow a little margin of safety.

Then consider some travellers may have a long distance to get to the airport. They might need to depart home at 04:00 or 05:00. But at those times there may be no practical public transport options. Maybe a taxi is viable but a lot more expensive.

And it might mean rising nearer 03:00, even staying up overnight (and suffering later for doing so), or risking alarms that do not go off, or moving near to the airport the evening before and staying in a local hotel (more cost).

Compare that with say an ETD of noon and it is a lot more hassle and possibly expense. So noon is more popular, so passengers are prepared to pay more for noon than 07:00, so airlines charge more for noon than 07:00.

The flight is quite short duration (~1-1/2 hr) so an 07:00 take off should give a full day in Sydney on arrival. But it is ~1,000 km and for most business people probably justifies eating into some of the working day (not that the weekend is!). "Sorry, I can't make a 10am meeting, make it 11:30" is probably easy to accept coming from someone having to travel that distance (on a flight at a more civilized hour).

Your example is however a weekend, which is a special case. From Sunday afternoon onwards one can expect much higher numbers to want to travel to Sydney than on a Sunday morning. That is, business travellers based in Brisbane preparing to work the Monday in Sydney (who do not want to give up too much of their weekend in Brisbane to do so) and leisure travellers having to return home to Sydney (who do not want to cut short the amount of time they spend visiting Brisbane – nice place!).

I've almost convinced myself that nobody would want to travel at 07:00 on a Sunday :)

It is not that strange – times of peak demand can lead to higher prices then for public transport, telephone services, electricity, oil, theatre tickets, drink and goodness knows what else.