In my experience, jobby job (often spelled jobbie job on the web) means a crap job, McJob, something to allow you to pay rent, but the web offers other definitions as well (like here). I figured, half-consciously, that it was reduplication with the diminutive -y on the first element. We have similar patterns from kitty cat to chinny chin chin, of course.
But part of what's fun about word histories is the little wrinkles they show on close examination. If you look around on the web, some people (a commenter on the link above) see the origin of the term in Snoop Doggy Dog's classic video for "Gin and Juice" (which you can watch here, with Dr. Dre making a guest appearance), where his father says:
Snoop Doggy Dog, you need to get a jobby job.
So, it's playing off of his name, but the name is built on the old pattern, I suppose. In fact, when his mother is trying to wake him up, she's yelling "Snoopy" to him.
Of course, there are other names of this sort. Those who work in the framework of Presidential Grammar will have long since thought of the Bushian nickname for Vladdy 'KGB' Putin, Pootie-Poot.
Wonder if this pattern will take off? Or maybe it's more widespread than I realize?