Thank you all so much for your responses. I think the poodle seems to suit best, and grooming requirements are not a problem. I don't know much about poodles and tend to get oput off by photos of them looking rather strange after weird grooming, but photo's you provded here looked lovely. They sound like lovely dogs and very suitable. I'll show my friend these posts.

To those who made me laugh by recommending letting the dog walk, don't worry, my friend will love to walk the dog. The reason she wants one that will fit into a bag is for ease of transport, not to be carried instead of using the four legs provided with.
I was also looking at pugs. They seem to be adorable dogs. Of course they are too big for a bag, but I never knew how adorable they were. Thanks for all your photos too - all the dogs are so gorgeous and obviosuly have wonderful loving homes. I'll also suggest giving an adult dog a home.

Thanks again!