I don't think it is a good idea to breed Chewie. Where I live (NZ) most people spay there dogs at 6 months, I know very few pet dogs that have not been spayed (the only one I can think of is a male labX and Skye was a relatively late spay because her owners could not afford it and were on the city council waiting list to get it done for free, she was done at aound 18 months).
Getting your dog speyed is pretty much a given for most here (unless definite breeding plans are already made - that mostly includes working dogs, pedigree dogs, puppy farmers and back-yard-breeders), when Holly was doing her puppy obedience nearly the entire class had to have the same week off because they had all reached 6 months and were all getting speyed/neutered that week.
We have to pay registration for our dogs every year and you get a discount if your dog is speyed/neutered. So speying/neutering is big here.
Considering that most dogs here do get speyed (and most at 6 months, well before they could/should have a litter) if there was a significant health risk I would think it would become fairly apparent. I don't think there is a higher incidence of any cancers etc in NZ compared to countries that don't have such a large "spey/neuter culture" (other than perhaps skin cancer due to the hole in the ozone layer
). There is also relatively few dogs in rescue here, there is a much greater problem with cats.
I don't think having a litter is really protective against health issue, and even it were very
slightly (I don't believe it is, I think having one litter is an old wives tale), I don't think it would be worth it concidering all the thinks that could go wrong during a pregnancy/birth/the future of the pups.
Some more personal/selfish reasons:
The things that really put me off ever breeding any female dog that I will ever own (mutt, pedigree or any dog) is the potential complications that could happen with a pregnancy. For example, I would not want to risk Holly's health and
life just to have puppy's, she is sooooo much more special to me than any litter of puppies that do not exist.I also would be worried about how having a litter could effect her personality, she is my baby. My baby can't have babies.
Dogs can and do die during pregnancy/birth. Sometimes they have complications that require surgery. A c-section is pretty traumatic and could kill the dog, cause an infection, could cause incontinence issues in later life. Sometimes all or some of the puppies are born dead (I believe it's pretty common to have at least one dead puppy in a litter). There is more to breeding dogs than it sometimes seems, especially if any complications occur.
An additional reason that I would not breed Holly is I know nothing about her parents. This worries me about all of our dogs actually, I don't know what their parents health is like: are they even still alive? do they have all their teeth? should I expect any of my dogs to go deaf when they are 5 years old or develope cataracts?
When we were looking at getting an adult dog, before we met Lewis, we visited a 4 year old shi-tzu X (orginally from a petshop) that needed a new home, he was a very nice dog. His owners had said they had been contacted by some puppy farmers who were willing to fly him to them etc at their expence.
His owners wanted him to go to a family so they got him neutered before trying to re-home him again. The bit that shocked me was that this 4yo dog had bearly any teeth left! He had just been at the vet/dentist getting another tooth removed. He was only 4, he had a good home but most of his teeth were gone and yet if he had gone to one of those puppy farms who knows how many puppies he could have passed his truely awful teeth to?
So, although Holly (and Chewie) has perfect health at the moment, we don't know what their parents health was like. And when you select the male dog to mate with you have just multiplied the problem (especially if you use another mutt). It also means that you don't know what sort of recessive disoreders are going to show up in the offspring when you double up on genes in the offspring because you don't know what is lurking in your dogs ancestry. If you get unlucky the puppies could be born with so many awful things wrong with them. You would be blindly playing with genetics.
I would also worry about where the puppies ended up. I think I would have a very dificult time selecting homes that are good enough. And would worry about the puppies forever.
Anyway, that's my personal opinion
I hope it hasn't scared anyone too badly. I just know that aside from the moral dilemma of adding more puppies to the world when there are so many without a home, there a lot of reasons that I will never breed any female dog that I own. I would rather let somebody else accept the risk if they choose to and just buy/adopt a dog/puppy.
And as much as I'd love to, I'm not going to risk taking a dog off the street and bringing it home in case it attacked Chewie!
I'd already seen that site and I kinda feel it's biased towards the 'no breeding' side and I was really hoping for something more balanced.... But I understand this is a very emotive subject and people tend to sit very firmly on one side of the fence! 
