How long does it take for the wolf to have puppies after you mate on quest?

It seems you're asking about the "Wolf" companion in the video game "The Elder Scrolls V: Skyrim."

There is no mating mechanic in Skyrim, and your companion, the wolf, cannot have puppies.

Companions in Skyrim are purely for combat assistance and don't have any further interactions like breeding or having offspring.

If you're interested in playing with wolves in Skyrim, you can try looking for mods that might add this functionality. However, be careful as mods can alter the game's functionality and stability.