I believe the quest is first offered when you get to Level 8. You get the dog after you have 15 friends at 100 friendship points. The dog is supposed to stop others from stealing your crops, but it doesn't stop everyone all the time.
Even though I am level 18 in CS, I just got the dog last night. I don't expect it to really stop anyone from stealing, but I was just glad to get that nagging mission off my to-do list!