Hi there, you are through to Dr. Jake. Im a UK based vet. im sorry to hear of your concern with your dog, Koda. we see diarrhoea commonly in young puppies when they go to new homes, there could be a few reasons for this.
moving to a new house for a puppy can be stressful and stress related diarrhoea can be occurring - using adaptil plug ins and pet remedy sprays can help while they settle in
if you have changed the food the puppy was on, or have added in new treats or snacks since picking the puppy up sometimes new food items can cause this as the body isnt used to these new foods or treats, sometimes they can be quite rich especially for a young puppy.
other common causes of this in puppies is intestinal parasites, hopefully the breeder has wormed the litter prior to passing them on to their new home and if not, i would recommend getting some treatment from your vets.
this may resolve over the next 24 hours though if it doesnt i would recommend making an appointment with your vet for a full examination and some medications to be given, this usually consists of pre and pro biotics to help replenish the healthy bacteria in the gut and help bind the loose stools. if koda hasnt been wormed recently then they will also be able to provide you with some worming treatment
the red colour may be a small amount of blood, this isnt a big concern unless a large amount of blood is present
i hope all this information helps