I think these little bench top lathes are good for making small parts and I've made some close tolerance miniature bushings on one but most of the lathe work needed for a car will require a bigger lathe. You should be able to find a small used floor model for around $800. You get better deals at an actual auction than an ebay auction on used machinery and shipping won't be so bad if it's closer to home. If your hobby was model railroading the mini lathe is great but for a hot rodder it would be a $400 dust collector taking up space on your workbench.
And Rob is right about getting as much tooling as you can with the lathe that you buy. It should at least come with a 3 jaw chuck and a tool post. A set of collets would be nice but aren't always included.
AL