Yes, there were several breeds of pre-columbian digs in both North and SOuth America. The accepted wisdom amongst palaeo-anthropologists is that by 10,000 years ago every human settlement on Earth had domesticated dogs, with only a handful of possible exceptions. What breeds I’m not quite sure, but almost certainly the huskies, samoyeds etc. would have pre-columbian roots. The California Dingo is almost certainly also a throwback from a domestic dog even though the Dingo itself is now classified as a wolf.
The reason why domestic cats haven’t gone feral in a big way in North AMerica as they have in Australia has a lot to do with Australia’s ecology and wild life.
It is now gaining increasing acceptance that cats were in Australia prior to European contact, probably brought in by Maccasans during their annual trading voyages to the Northern Territory.
At the time of the arrival of the first humans in Australia there were only about 5 large to medium sized mammalian carnivore species or genera. This compares to about 25 in the contiguous USA today, an area of approximately the same land area. There were many more species when humans arrived. The same array of large carnivorous mammals is true of every other similar sized landmass outside of Australasia (ignoring Antarctica).
When Europeans finally arrived in Australia, and probably by the time the cat was introduced, the native large-carnivore assemblage had dwindled to only two species on the mainland : the introduced dingo and the spotted quoll. The reasons for this poor representation of carnivorous mammals is largely due to an erratic climate, allowing mammlas to be largely supplanted by reptiles, of which Australia has an abundance. When the cat arrived the Australian ecosystems had been severely disturbed by Aboriginal and management practices and the introduction of the Dingo and several diseases, leaving gaps in the food chain that no native animals had been able to fill. This meant that an opportunistic carnivore like a cat could move into the vacant niches. Even so there are few records of feral cats in Australia prior to the 1850’s, despite cats being indisputably introduced to the continent in the 18th century. The reason for this delayed spread is probably that cats aren’t very good predators on Australian species compared to our native animals, in fact they suck. Contrary to popular belief Australian animals have extraordinary defences against predators, and non-Australian carnivore species basically aren’t in the running. Cats are just too clumsy and impatient to effectively hunt Australian animals used to coping with huge numbers of expert stalking reptiles like goannas, snakes and terrestrial crocodiles in addition to quolls.
What changed in the mid nineteenth century was the sudden explosion in numbers of an animal that cats are very good at hunting: rabbits. This allowed cats to support a large and acclimatising population that could sustain itself during years when rabbit numbers were low.
In the USA of course domestic cats face very stiff competetion from six locally adapted cat species, in addition to a suite of other predators including canids, bears, raccoons civets etc. The ecosystem in the USA has also not been as disturbed as in Australia and the native species are pre-adpated to all the ecological niches. Added to that there are no introduced plague mammal species.