By Caroline Cheese
BBC Sport at Wimbledon |
Kucova knocked out the top seed in the opening round but 17-year-old Cavaday proved too strong.
The Kent left-hander faces Poland's Urszula Radwanska, the sister of last year's champion, in the last eight.
There was disappointment for Julia Bone of High Wycombe who lost 6-2 6-1 to third seeded Russian Alisa Kleybanova.
Cavaday made her senior debut at Wimbledon last week as a wild card, causing Ai Sugiyama problems with her powerful serve.
"It can cause a lot of players a lot of trouble," said the teenager.
"I always say, if I'm serving well and I'm hitting my spots, I've got a chance against anyone.
"It's a massive weapon. I've got a long way to go with it. It can still be tons and tons better."
The last British players to reach the quarter-finals in the girls' competition were Elena Baltacha and Anne Keothavong, who both went on to reach the last four.
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