Should I attribute the font designer on a piece of artwork?

I assume you mean fine art, not commercial art. If yes, then yes I would credit the foundry or typographer.

You’re the artist, and you have license to do as you please. I doubt you’ve got a copyright issue unless your art is mainly just showing someone else’s font. Many people who sell fonts do have terms of use agreements, which would cover what they want you to do. But if it’s art, then I’m sure almost all works of art than just have some print in them do not mention who designed or sells the fonts. Maybe the IP ape-tards involved in “the digital arena” are trying to change that. (I’m not a lawyer – does it show?)

Unless there are specific license terms that came with that typeface indicating you should, then I don’t see why you shouldn’t.