Mosquito Net
A mosquito notebook, for some reason, is a mosquito net. Think of a notebook with graph paper lines on it, perhaps. These lines are shaped like a net. Surround yourself with it to make your own mosquito net.
かや
The first kanji, 蚊, uses the reading you learned. The second kanji has an exceptional reading, や. To remember や, think about how you had to take a giant mosquito net and cover all of Yankee (や) Stadium. They have a rough mosquito problem.
十人用の大きな蚊帳はありますか？
Do you have a mosquito net big enough for ten people?