MELBOURNE (Reuters) - Mirjana Lucic-Baroni could barely contain her joy after continuing her remarkable run at the Australian Open to reach her first grand slam quarter-final since the 1999 Wimbledon championships on Monday.

The 34-year-old, who won the Australian Open doubles with Martina Hingis in 1998 at the age of 15, bounced up and down with fists clenched in triumph after dispatching American Jennifer Brady 6-4 6-2 in little over an hour.

Personal problems, including alleged abuse at the hands of her father, cut the heart out of her career but Lucic-Baroni has battled her way back from the very bottom of the game after returning to tennis in 2008.

Still bubbling after matching her best grand slam performance 18 years on, Lucic-Baroni sent out a self-censored message to other people struggling to fulfill their dreams.

"Eff everything and eff everybody who says you can't do it, just show up and do it with your heart," she said.

"I'm a tough little cookie and I'll work really hard and do whatever it takes to get where I need to be, I can't tell you the satisfaction I feel right now.

"Really incredible, I've worked so hard ... I hope nobody's going to pinch me and wake me up because this is just incredible."

Lucic-Baroni won her first singles match at Melbourne Park in 1998 but had to wait 19 years for her second victory in the year's first grand slam last week.

The German-born righthander's Australian Open campaign, which also includes an ongoing title bid in women's doubles with Andrea Petkovic, has been achieved despite a nagging leg injury.

Lucic-Baroni had no doubt that she would be able to fulfill her quarter-final date with Czech fifth seed Karolina Pliskova or Australian Daria Gavrilova.

"No way, I'm not giving up. I pick up a couple battle wounds every time I play," she said.

"So next match, I may have a few more straps on, but I'll carry on."

Now ranked 79th in the world, Lucic-Baroni overpowered Brady on a steamy day on Margaret Court Arena, dominating from the baseline and blasting 35 winners past the qualifier.

While the 21-year-old American, making her singles debut in Melbourne, will have plenty of other opportunities, Lucic-Baroni credited the support of her family for helping her grasp a second chance.

"I'm really blessed," she added. "I've had a really rough patch early in life but I'm really blessed with the family I have."

(Reporting by Nick Mulvenney, editing by Amlan Chakraborty)