The 24-year-old American, who made the fourth round of a grand slam for the first time on Saturday with a surprise 6-3 6-2 victory over compatriot Coco Vandeweghe, was lucky to be in Australia at all.
She was only given the all clear to travel in early January after she had a tumour cut out of her knee in late October.
"It obviously was not a fun time hearing that," Brengle said of being told the spot on her knee that she discovered before last year's U.S. Open needed to be removed.
"But you deal with it. A lot of people have to go through so much worse.
"They found it really, really early. We took care of it (and) I have a nice scar on my leg to show for it."
Cancer organisations in Australia and New Zealand, which have some of the highest rates of melanoma in the world, encourage people to 'slip' on a shirt, 'slop' on sunscreen and 'slap' on a hat during the summer months.
Brengle said her own cancer scare should be a lesson to warn of the dangers of being out in the sun for extended periods, which is an occupational hazard for professional tennis players.
"I think it should probably be a little bit of a wake-up call to people to wear sunblock when you're out there," she added.
"I think it's part of being out in the sun. I mean, I'm not the tannest person in the world. I get freckles. It happens.
"(But) they caught it quite early. As long as the margins are clear when they take it out, you're good to go.
"I'm reapplying the sunblock, but I'm totally clear."
Brengle, who made the final in Hobart after playing qualifying in Tasmania, will move inside the top-50 after the Australian Open and said she felt she was now in an upward curve in her career.
"I've been decently confident for a while now," she said. "I go out, and I'm trying a lot to play to win instead of being afraid to lose.
"As long as you go out and you play to win, do your best, you can walk off court with your head held high."
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
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