I am a vet, and I would also say your vet is misguided! Six is far too old for a dog to have a first litter, you would be putting her at serious risk of complications. Also, if she is herself a rescue dog, that is another no-no in terms of breeding. Everyone thinks their own dog is wonderful, but the only way of knowing if a dog really is an outstanding example of their breed is by having them judged objectively against others, by showing them to ensure they meet the breed standard for conformation and temperament, or working them in the capacity they are bred for. Behavioural issues like separation anxiety should also automatically rule a dog out for breeding as this is not sound temperament.
Breeding dogs, when done responsibly - and it shouldn't be done any other way - is not for the faint hearted. It is expensive, incredibly time consuming and potentially life threatening for the bitch. Puppies often die, sometimes after you've nursed them day and night for weeks, it is not easy. Emergency C-sections, which are not at all uncommon, cost in excess of £1000 - more if they are in the middle of the night, which is when most dogs give birth! - and are not covered by pet insurance. You are also responsible for the pups for their entire lives - would you be able to take 1 or 2 or 3 of them back 6, 12, 18 months, or 3 or 4 years down the line? Or would they end up in rescues as so many other thousands of dogs do every year.
You also have the cost of health testing before you breed the bitch - most breeds need a clinical eye test and hip scoring as a bare minimum, and most breeds also have DNA tests for specific conditions. Your local vet telling you your dog is healthy is not enough, there are a huge number of serious genetic conditions in various dog breeds, and the only way of knowing if your dog carries them and could pass them on to offspring is to have them tested.
If I had a £1 for every time I've had someone come in to the surgery with puppies they can't find homes for and tell me 'but I had 10 people say they wanted one before they were born!' I would be able to retire aged 33. The idea of getting a puppy often seems great to people, but when confronted with the reality a few months later, they change their minds!
If you are going to spay her - which I would recommend - then as others have said, 3 months from the last season is the ideal time. It's really good that you've asked the question though, you're obviously a good and caring dog owner.