I've never had problems with Gus eating so I'll leave that for someone with better ideas.
I have a car seat for Gus because he gets carsick but what is really important is having them in a harness and strapped to the seatbelt. What you are doing is fine as long as the leash is secure and not too long. Imagine slamming on your breaks, how far forward would she go?
The do sell straps designed to attach to harness and seatbelts. They also make car harnesses with extra padding for added safety. I got mine at Petsmart (I think it was $9.99). Hope that helps.
I'm a safety nut so I have to add if you have airbags you might want to make sure she is far enough back not to be hit by it or put her in the back seat.