We're not sure why poor dogs always seem to get used to describe something really dreadful, but it's the case with doggerel — meaning irregularly rhyming, really bad poetry, usually comic in tone and fit only for dogs.
Sometimes doggerel has a non-critical meaning: plenty of popular comic poets (like Lewis Carroll or any limerick inventor) had no aim to make great art, just great light verse, and they succeeded brilliantly. They were masters of doggerel. But pity the earnest highbrow poet like the immortal Scotsman William McGonagall whose doggerel was so bad his audience frequently pelted him with eggs and rotting vegetables. Now his poetry was only fit for the dogs.