Linking to an offsite video is fine as long as the host site is appropriate (i.e., don't link it to an adult video site) and the content you are linking to doesn't violate site rules. There is not a way to place music directly onto pet profiles.

No, you may not falsely attribute copyrighted content to yourself, a pet, etc. All copyrighted content must be credited.

When it comes to rule questions, especially those that are quite specific, it's best to file a support ticket. We'll be happy to help you further from there! :)