What a worry for you. I don't think antibiotics work, Molliepops, because kennel cough is a virus... Although... at the back of my mind, I think I've heard there are several types of kennel cough so maybe it can be a bacterial infection and in which case antibiotics would work.
Halewood, I'd be concerned that the animal is only 10 weeks old, though - may not have the reserves to cope with a bad infection. Have you been in touch with the breeder? Because if you've only had the pup for 2 weeks (not recommended for puppies to leave mum before they are 8 weeks old at least) I'd be expecting the whole litter to have the disease. It might be useful for you to know what the breeder would recommend - though I realise the bug could have been passed by your existing dog.
I once had two adult dogs with kennel cough - after having the live vaccine - and they had it quite badly in that they sounded awful. But they didn't stop eating... labs don't.
Good luck and hope the pup gets rid of the bug without too much problem.