I bought Lottie a car harness last weekend, she was nearly 10 weeks.
She is still quite a little girlie though for her age, but I got a Hi Craft dog car harness and it is extra small.
If you measure around the pups chest the harnesses seem to go by this size. As I said Lottie is little and the extra small is ample, she has stacks of growing room.
I got it from Pets at Home and they were happy to let us try it on her or exchange it if it was the incorrect size.
Hope that helps.
BTW, she sits quite happily in it, and has even been on the back seat alone in it with just me driving and happily settles down and goes to sleep.