Puppy and Poochie were half-siblings
The reason Puppy and Poochie were such close friends is because Jakob was actually Puppy's father, which is also why his death affects Laika so much compared to the deaths of other characters. Whether this was because he and Laika were in love or out of necessity due to a lack of desirable male partners in Where We Live despite the Elder's mandate for Laika to bear more children is a mystery.The curse causes Laika's maternal bloodline to reproduce independently of a male partner
An alternate explanation for the absence of any explanation toward Puppy and her dead sisters' father(s) is that they simply don't have one, and the curse causes children to gestate periodically in the current curse-bearer's womb until one of her children survives the fever. This would also help to explain why Laika nor any of her ancestors ever seem to have birthed a son, as it's another effect of the curse's influence.