Hmm...I almost want to say the owl pup is Schuyler's, but I'm having trouble making this hint fit:
I stand out from the rest of my litter in a way that might not be obvious from my pup stageThe owl is far too obvious right now, it has a pretty distinct line art edit. Unless what it means by
'might not be obvious' is that, even though it does have that facial edit, in the grand scheme of the staff litter it might seem to blend in. Hmmmm....
Okay, I'll take a crack at making this guy fit the hints I suppose.

"Pretty bird"
This one is pretty obvious; it's an owl, and owls are generally seen as pretty birds.
"An aspect of my dog follows a logical progression as it grows"
The marking on its shoulder looks a bit like a wing. It could develop wings later on.
"The reds and oranges were my favorite colors in the palette this year. They remind me of fire!"
This pup uses only the fiery colors of the palette.
"My dog's eye color doesn't match the palette"
Its eyes are blue, which isn't on the palette.
"Perhaps the wandering sun could help"
This one is a bit tricky to match up. Owls are nocturnal, so the sun isn't really related to them, but maybe 'wandering sun' in this context could mean setting sun?
"I stand out from the rest of my litter in a way that might not be obvious from my pup stage"
Okay, after rethinking this, I think this might be referring back to the 'logical progression' hint. Even if it's not obvious now, something on this pup (wings, perhaps) will show up on the adult, setting it apart from the other staff dogs.