Is it worth upgrading from a Nikon D5100 to a D7000?

I love my D5100, but my complaint is that it doesn't have a built-in focus motor. The lenses are expensive, I'm starting to think it's more advantage to pay more for a body and pay less for lenses. What do you think, will I get a lot in return with this upgrade? And will my AF-S NIKKOR 50mm f/1.8G work on the D7000? It's basically the only lens I use. I'm mostly a portrait photographer.
I would have paid half the price for this lens if I had a D7000.

Yes, the D7000 has a built-in auto-focus motor which will allow you to the older Nikkor AF and manual focus AI lenses, but in reality, the fastest auto-focus lenses made by Nikon are the AF-S lenses which can be used on any current Nikon dSLR.

I'm in the habit of buying only AF-S lenses for my Nikon system, even though all my cameras have built-in auto-focus motors. I do that because I shoot a lot of sports and action photography and need the faster auto-focus AF-S lenses give me

Not sure what you mean by you would have paid half the price for the lens if you had the D7000, but, yeah, of course, your 50mm lens will fit the D7000

Yes. The Nikon D7000 is more advanced than your current camera.
I considered the Nikon D7000 a while ago, but I ended up with my beloved Nikon D600. It serves me well. I never thought about buying any other camera.
About the lens, sure it will work.
However, I don't recommend the older Nikkor AF and manual focus AI lenses at all.
I always buy AF-S lenses. They are higher quality and auto-focus faster.