My friend had an accidental mating last week with her 7 month old puppy. She is planning to DNA test the pups to see if he is the father of any of them. We have had a look on the KC site but can't see if there is a minimum age for the father of the puppies. If he  does turn out to have fathered any of the pups will they be able to  be registered if the father is only 7 months old?

Yes, they will be able to register the litter still, as long as the Sire is KC reg, age does not seem to matter (with regards to Sire) to the KC at present. :-)

Would they not consider the mismate injection instead of bringing a litter of pups into the world where the sire is 5 months too young for official health checks?

In some circumstances then yes you would be right to suggest the mismate injection but  in this case they have decided to go ahead with  the pregnancy.
The bitch was mated as planned to a champion dog and the litter had been planned for quite some time. Lots of people are waiting for puppies. Almost a week after the first mating to the planned  dog she escaped and tied with the youngster, only about 2 days before her season finished. It does seem as if there is hopefully not much chance of any resulting puppies being sired by the wrong dog but of course my friend wants to be absolutely certain, hence the DNA test.
, The youngster is the same breed, and well bred from health tested parents, is not too closely related to the bitch so my friend has decided that she  will take the chance and let the pregnancy continue.

Fair enough, I would do the same in the circumstances.
Good luck for the outcome.

Should the young dog be found to have sired the litter, the problem I can foresee is that as he will have been too young to be hip/elbow scored and health-tested, the pups will only have half the health checks required for most breeds.

I suppose a clause added to the puppy contract of any puppies by the youngster giving some sort of facility for a refund etc if a health issue arises with regard to him being untersted, and promise of sire health screening and details as soon as he is old enough. 

It would only be a month or so after the pups are ready for homing that the tests could be done.

This is a small breed which is  not usually hip or elbow scored  so that is not a problem. If any of the puppies turn out to be from the youngster then the prospective owners will be fully informed about how the litter was conceived.

Oh this occasion I don't think we can ask anymore of the breeder :-)  good luck and I pray they end up all out of the intended one :-)

I concur - let's hope that the No 1 stud is the daddy - and hasn't been ousted by a young whippersnapper!