I think it would have to be  a "special" dog, like a dalmation or chihuahua (is that how you spell it?) because if you where wanting to have it be a certain dog - and not a dog a person can "build" - it would have to be something different so the player can easily see that it's what they are looking for; however, if you would change it to were you can "build" a dog and bring it back to the Old Coot - I wouldn't suggest endgame gear or I would suggest more challange, which I'll explain:

If it is finding a specific dog, I wouldn't do a completely random spawning, I would make it to were it could spawn in towns/revisitable locations (like the ranch) because speedrunners might want to have something other than "click the explore button 30 times" - Now if you make finding the specific dog a set location (like one of the shacks in Anchor Rage) I would suggest having a little girl have it/found it and you have to take it back - either diplomatically (like a trade of microchips so she can make a robo-fido) or by stealing it while she is gone (which would mean stealh may need to be implemented).

If it could be "building" a dog and giving it to the Old Coot, I would suggest a mini-boss fight (cause he is off his rocker) or another side quest for it (like getting microchips for him because he needs to make it a cyborg or something).  A mini-boss fight would be cool, like skelly-dogs coming out of the dirt around the house (which could be explained with the Old Coot saying "looks like the other ones are jealous") or a mini-boss fight with the Old Coot, but I don't how you would explain it other than "oh he's CrAzY who would of known?!". Now having another sidequest like getting microchips for him, by getting more dogs (which may be a bit too remincient of the cat lady quest), or by defeating roaches/a raid at his home because "my dog don't feel safe with so many bugs around".

Now a raid at his house whenever you give him a dog would be a good idea, with all the enemies/roaches/sand crawler/other bugs targetting the dog you gave him (this could be for either finding the dog or building the dog for him, but if it is building the dog you can try again). Obviously you would have to do quite a bit of monsters to justify end-game gear for a dog, and you would have to do good walls/defences/build that isn't suspious to the player before the raid happens so it is fun to do the raid by dodging and ducking between walls and stuff. You could also have it to were only the player deals with it (no help from any partners) by making the Old Coot say "I'm not gonna give you that reward sonny boy - if your posse  are around to see it." Handling a major raid by yourself could be a really cool thing, especially if the stake is a dog (and your reward of course)