Hi. I'm hoping someone can help me out with remembering what these toys were called.
They were dogs and pups, about 2.5cm to 5cm high. They had shiny fabric bodies that were filled with beans, and had plastic heads. The important part about them is that they came as a set - there would be one adult dog and two babies that you could see in the packet and then there was a 'mystery' box that had another baby of a different colour. For example, I had a blue mother dog with two blue babies. When I opened my mystery box I got a red baby. The idea was to collect each of the sets to complete the different families.
Someone on the MLPArena (I think it was VanillaScoop?) reminded me of these a while ago, and I am borrowing her picture:

Her picture is of the two babies from one family (they originally had a white spotty mother as well) and the yellow baby that came in the mystery box.
I borrowed this picture from ebay. It shows the blue mother dog that I used to own, at the centre front of the picture.

I got my set during the 90's, around the same time as LPS. I honestly haven't the faintest clue of what these might have been called.