Hi. I've adopted Sophie from Windhelm, and she's been with me living the high live in Solitude with me for about 2 in game weeks now. She has not yet brought home a pet yet though. How long does it usually take for your child to find a pet?

That said, she does not leave the city at all. I would think to get a pet you'd have to leave the city walls, am I right? Or one day will I just come home and she'll have a pet ready? I would go get my own dog but first I want to let her bring her own pet to see what she chooses.

It's completely random.

Lucia supprised me once. First time ever adopting and I come home to find she has a fox.

To facilitate the process, I recommend taking lots of short trips, maybe 2-3 days in duration. Every time you return home after a trip (unless it's too short), a child-related event is triggered: a gift, a request for a gift, an allowance request, a fight with a sibling, or a newly adopted pet. Do it enough times, and odds are you'll get a pet soon enough.

I have four characters with adopted kids, and three have pets (two foxes and a skeever).