First try - Little Willies

After more thought, another way to mend the end of the first staza would be to ADD unstressed syllables to the penultimate line so the couplet is more even. Get a little smut into it too if you want. My version would go something like

Doodles Duncan, big and fat,                         (X x X x X x X)
Squashed his Grandma's ginger cat.            (X x X x X x X)
Now her pussy haunts his waking dreams  (X x X x x x X x X)
Doodles eats until he splits his seams.        (X x X x x x X x X)

This still gives you four feet per line but moves more predictably in the last line without changing that particular line at all.

You'll spot I changed kitty to ginger. I wanted a word that worked more for its living - ginger cat is a stronger image to me than kitty cat. it could equally be tabby, black tom or persian. But you'll want to find words that work for you of course.

I like Stephent's idea of an extra verse, though I'd be tempted to add a single couplet with a twist to it, followed by your threats to the reader.