Julie (and her entire order at large) are very kind people, and are willing to help out just anyone.
Julie Farkas is a doctor, though you'd know that if you've already visited the Old Mormon Fort and have spoken with her before. Upon reaching the Old Mormon Fort (also located in Freeside, as you likely already know), seek out Julie. The King suggests that you speak with Julie at the Old Mormon Fort to learn more. His body makeup is quite complicated, and not everyone is skilled enough to deal with him. Indeed, Rex may be on his last leg, and nobody has been able to help him out. The King will explain that Rex hasn't been quite right for some time. Amongst them is his mysterious bionic dog, aptly named Rex. Upon concluding that side quest, you'll be able to talk to the King about all sorts of issues. Blues, and it's undertaken in the name of The King of Freeside. The Side Quest in question is called G.I.
This is one of the rare side quests in the game that can't be earned until another, far lengthier and more detailed side quest has already been completed in its entirety.
