It's not. I was wondering this too a while back and did some searching; it's still broken and likely will stay that way until the new source.
It should be the quest "Kenta's Advice" Really hope this quest can be fixed, this was a really useful quest to make your pet's walking speed match your own.
yea it would be awesome, its kind of annoying to see the pet constantly drifting off. Well I'm sure it'll be fixed eventually
What I could find regarding this quest is that this effect is not specified directly as a reward. It does say in the quest text that the pet will be "following your each footstep". For this effect to happen your pet had to be of a certain level, which I thought was 15, but I might be wrong it has been a while. I did find a video that explains this quest in more detail: