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I want to say "My cat is snoring!" I found the verb to snore is 「いびき」and Jisho.org says it's a "godan verb with ku ending". I haven't learned what that means, so I tried the -ku conjugations from Wikipedia, but nothing lead to "is snoring," at least according to Google Translate. The closest I got was 「うちの猫はいびきいた」, "my cat was snoring."
What am I missing?
According to the dictionary, いびき is a noun:
いびき【鼾】snoring
http://dictionary.goo.ne.jp/je/4267/meaning/m0u/%E9%BC%BE/
There is no such a verb as いびく.
In order to make it into a verb, you have to say 鼾をかく.
http://dictionary.goo.ne.jp/edc/16000261601/meaning/m0u/%E9%BC%BE%E3%82%92%E3%81%8B%E3%81%8F/
So it becomes
うちの猫はいびきをかいている。
The verb ibiku used to be a regularly conjugating verb that had the same pattern as 引{ひ}く, apparently derived as a compound of 息{い} (more commonly iki) + 引{ひ}く. My big copy of Shogakukan's 国語{こくご}大{だい}辞典{じてん} lists this as a 四段{よだん}活用{かつよう}動詞{どうし}, the predecessor to modern 五段{ごだん}活用{かつよう}動詞{どうし}. This generally refers to verbs that fell out of common use before the modern era. In this case, ibiku is not used any more, but the stem and noun form ibiki persists. As other posters have noted, this noun requires the verb kaku (roughly, "to scratch out [a snore]"), or (less commonly) tateru ("to put up [a snore]"). In a pinch, you could say ibiki o suru and people would understand what you mean.
The entry mentions 「鼾｛いびき｝をかく」. The verb you need to conjugate is かく. いびき itself is a noun.
My cat is snoring!
= うちの猫が*いびきをかいている！
*Use が, not は.
To sound casual and colloquial, you could say:
うちの猫、いびきかいてる！
leaving out the particles が and を.
