This is a very small side quest that completed as soon as your team can return to the town of Dollet. The quest involves the Queen of Card’s son and her son’s dog and it has to do with the bones that her son has been graffitiing on to the grandfather’s paintings. The bones that he paints indicate the spot in Dollet where you can find the dog and receive a reward.
The rewards for this quest are not super important. Early on in the game they consist of a 
Potion, a Phoenix Down and a Soft, but if you return to Dollet in Disc 3, the rewards will improve and become an X-Potion, Mega-Potion and an Elixir.
If you have just completed the Timber Forest Owls Mission on Disc 1, you can complete this side quest now and get it out of the way, but consider returning to complete this later on in Disc 3 for the better rewards noted above.
The ideal time to complete this is after you have access to the mobile Balamb Garden ship and have left Edea’s House. The walkthrough section of this strategy guide references it on the Locating the White SeeD Ship section.
You need to complete one step with the Queen of Cards before you can begin this quest, namely, you must speak with her on the top floor of Dollet Pub and ask her about her artist father.
After you have done this, you can access her grandfather’s house which is where you can find her son to kick the quest off.
Exit the Dollet pub and come further down the street, towards the camera, and speak to the the Queen of Card’s son standing outside of the house in the next screen. Follow him in to the building when he gets up and leaves.
Have a look at the painting, which the son has plastered over with a picture of a bone, and then speak to the son. Note that you may also want to challenge him to a game of Triple Triad to win any cards back that you have lost to the Queen of Cards.
If you’re completing this side quest during your first trip back Dollet, the Queen of Card’s son will likely have the the MiniMog card.
Triple Triad: MiniMog CardNote that the Queen of Card’s son will only have this card in his possession if you recently lost MiniMog Card to the Queen of Cards during your return trip to Dollet.
Now its time to complete the side quest. Leave the grandfather’s house and notice that the dog that was outside is now gone (Squall will say “There used to be a dog here…”).
You need to travel to the location that was showing on the painting that the son graffitied with the picture of the bone. Don’t worry if you didn’t recognize or memorize the location though, this quest is very easy.
Make your way back to the Town Square to find the dog on the right side of the screen. Interact with the dog and select “Look” when asked whether you want to examine whatever is underneath it and you’ll receive a Potion (or X-Potion if you’re on Disc 3).
Go back to the grandfather’s house again and look at the paining again to see that the next one has been graffitied as well. Speak to the son one more time and then head back to the entrance of the Pub to find the dog sitting outside of it. Check under the dog again to receive a Phoenix Down (or a Mega-Potion if you’re on Disc 3).
Go back to the grandfather’s house one more time, check the painting, talk to the son, and then talk to the dog which is now sitting just outside of the house. This last time it will have a Soft underneath it (or an Elixir if you’re on Disc 3).
What seemed to look like it would be a neat game of hide and seek with clues ends up being extremely easy. That’s it for the Dog and its Bone side quest in Dollet. Use the links below to return to the walkthrough, which you have likely completed either after the Timber Forest Owls mission…
Or if you completed them on Disc 3, you may have done so after finding the White SeeD ship:
