2 man professions

Ok for my first set I had my main (Engineering and Mining) and my shammy (skinning and herbing).

Now they are both 80 and I want to work on my second set.

Issue is: The DK has no professions, and the healy druid only has mining.

Should I get like enchanting(for de) and herbing on the DK, and get skinning on the healy druid ? Or just say screw it, get enchanting for DE and just go go go.

Every profession now grants a bonus or items that only the character with the profession can make use of. In most cases, this amounts to more stats. Definitely plan on giving all your characters professions at some point for this reason.