"See u next rnd Jen B," the world No.61 scrawled on the lens of the courtside television camera after upsetting Ukrainian fifth seed Elina Svitolina 6-4 3-6 6-3 in the fourth round at Melbourne Park on Monday.

Brady duly upheld her end of the bargain with a 6-1 7-5 victory over Croatian No.28 seed Donna Vekic.

"Bring it Jess," wrote Brady in response on the very same Rod Laver Arena camera.

Having made a breakthrough run to the semi-finals of last year's US Open, Brady's appearance in the final eight in Melbourne was not wholly unexpected - despite the 22nd seed's two-week stint in hard quarantine on arrival to Australia last month.

But the same could hardly be said for the late-blooming Pegula, whose career grand-slam win-loss mark before this tournament was a distinctly underwhelming 3-8.

That record is looking a lot healthier now.

Pegula's scalps at Melbourne Park this year include grand slam winners Victoria Azarenka and Samantha Stosur, and now Svitolina, who has often been saddled with the unofficial tag of' "best female player yet to win a major".

Now she gets to square off against her Fed Cup teammate Brady, who Pegula describes as "an awesome person".

"It would be super-fun to see," said the 26-year-old Pegula.

"We've all been pushing each other.

"Why not push each other into a quarter-final, then one of us be in the semis?

"That's what we're here to do.

"We're here to have fun and compete.

"If I can do it against somebody that I like, that I wouldn't mind if they beat me.

"Hopefully not. But if they did, why not?"

Brady is the only player among the group of 72 forced to endure a 14-day heavy lockdown on arrival in Melbourne to progress to the quarter-finals.

"A lot of people were complaining and I told myself I wasn't going to complain," she said.

"There are way worse things going on in the world than me being stuck in a hotel room for 14 days."

Vekic needed medical treatment on her heavily-strapped right knee early in the second set against Brady.

But she ploughed on and still gave Brady a few anxious moments before the big-serving American steadied to book her spot in the last eight and a date with Pegula.

"I'm super-excited for her making her first grand slam quarter-final," said the 25-year-old.

"The emotions that she's feeling; you feel like you're on cloud nine.

"We've played before and we know each other so well.

"I'm really looking forward to it and it will be a lot of fun.

"Everyone back home in America will be watching."

Australian Associated Press