MELBOURNE, Australia—Alize Cornet dropped to her knees on the hard blue court, clasped her hands and took a few moments to let it sink in. In her 17th trip to the Australia Open, her 63rd run at a Grand Slam, and two days after celebrating her 32nd birthday, Cornet finally qualified for the quarterfinals at one of the four major events in tennis. Cornet recovered after a second-set meltdown in the hot Melbourne sun on Monday to advance to the last eight at the Australian Open with a 6–4, 3–6, 6–4 win over two-time major champion Simona Halep. “It’s never too late to try again!” Cornet said in her on-court TV interview. “To be in my first quarterfinal. It’s a dream come true. “The journey goes on. I still can’t believe it.” Cornet led by a set and 3–1 before losing five consecutive games and 16 straight points as Halep …