As Miles point out, the FFXI wyvern was added to XIV as a minion already.

As for the job-companion... I feel that'd require DRG to be rebalanced, possibly in a way that most of players won't like.

If you look at Machinist though, you'll realize that it's pretty much the FFXI Dragoon's alter ego. The only difference is that the turret is not smart enough to follow you.