Is the name "Pet Rock" copyrighted?

Copyright is not the appropriate protection. It would be trademarked. The answer to that would be that you need to search (or have a trademark attorney do it for you) the trademark database.

None of the Web references that I have found about the Pet Rock go into the specifics of whether it was trademarked. IDahl made millions with the product so I suspect that it was.

As Marina said, a copyright would not be appropriate in this case.
However, Pet Rock is actively trademarked.

Would you say that that trademark would be ok to use in Ireland and the UK for a very different product then what that company is offering?

I would say so, and I would think the law would back you up if it is not trademarked in the UK and/or Ireland.

However, let me just say this: I am by no means a trademark lawyer, nor do I have any real knowledge of trademark law in the UK or Ireland. If you’re doing something commercial, you’re going to want to consult a lawyer.

Well I was just thinking of making a small ebay business selling pet rocks.

Oh yeah, you should be fine for that. You’re not marketing them as your own. And if you really want to cover your ass, you can put on your page Pet Rock is a registered trademark of blahblahblah.

I have found this very helpful with copyright questions.