Brain Teaser

I have a Page-A-Day calendar at work, besides the French one, that my boss gave me for Christmas. It has comics called, "Brevity," which I'd never heard of before, and some of them are funny. On the back of each page is "The Daily Extra."

Today's Daily Extra is this brain teaser. I figured it out without having to peek at the answer.

I am a 6-letter word.
Letters 6-5-2 spell out a drink.
Letters 4-5-2-3 spell out a fruit.
Letters 1-2-6 spell out a pet.
Letters 3-2-6 spell out a pest, which often gets eaten by 1-2-6.
What am I?

You can post your answer in the comments. If nobody gets it, I'll put the answer in the comments in a few days.