Mooney suffered a broken jaw in the nets last Monday, requiring surgery the following day after being hit by a throwdown from coach Matthew Mott.
She was spotted hitting in the Adelaide Oval nets again on Sunday, before Australia's final Twenty20 against England was washed out without a ball bowled.
With Saturday's T20 also abandoned after wet weather, it means Australia can retain the urn with a win in the Test by claiming an unassailable 8-2 lead before the ODI component begins.
England's cards are stacked against them.
They would need to win the Test as well as two of the three ODIs to regain the Ashes, or win all three ODIs if the Test is drawn.
There is also now renewed hope that Mooney could be part of that Test.
Medical staff have been impressed by her recovery from surgery and she is now a serious chance to play in Canberra from Thursday.
Mott confirmed they were now looking at her as a real possibility to return for the Test, where she could either open or bat in the middle-order.
"The last couple of days, the swelling around her face has gone down quite substantially," vice-captain Rachael Haynesd said.
"Just having a bit of a chat with her and checking in with how she's been going, she's feeling really confident.Â
"She had a hit today and also a run around and she's not in any pain.
"Without a doubt she's definitely got her eye on that Test match in Canberra."
Meanwhile Australia's plan to get cricket into Ellyse Perry was also scuttled by rain.
Perry was left out of Australia's team for the T20 part of the Ashes series, and has instead turned out for the Australia A side.
She bowled three overs in a T20 for Australia A on Friday, while listed at No.3 she did not get a bat when Elyse Villani and Georgia Redmayne chased down the target without loss.
Perry was listed to open on Sunday, but the Australia A game was washed out five balls into the hosts' innings after she sent down two overs with the ball.
It comes after Australia quick Tayla Vlaeminick was ruled out of the rest of the summer with a stress fracture in her foot, ending her Ashes and ruling her out of the upcoming World Cup.
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