Not much is known about baby monster Sunny the Owlbear just yet, other than he was rescued by Jules & Eyrun from Ferrin's House, they then quickly moved him into their house afterwards, and from there the following apply:
Sunny can be spoken to with the Speak With Animals spell.
Sunny wants to live the pampered pet life at the moment, being fed and loved on.
None of this changes the fact that this is not in indoor pet.
Sunny has been in a battle with a half-orc snooping around the house and likely been healed a lot by the Kuo-Toa Idol. It is possible there is some influence of the associated Kuo-Toa deity upon the owlbear now.
Sunny eventually became an “outdoor pet” since he could not be housebroken.
Sunny didn't get much attention and ran loose a lot, eventually wandering off from the Mirror House.
Jules & Eyrun departed Goldvale suddenly one day and zero hope remained of keeping Sunny as a pet at that time since they were removed from the continent, leaving Sunny alone.
By the time Jules & Eyrun returned from overseas a few months later, Sunny had been captured by members from The Cult Of Alden as a sacrifice. Jules led Urist, Alimir, Matilda & Vesper to the graveyard near the Shrine Of Hayte on a rescue mission to free Sunny. They succeeded, which resulted in Sunny dashing off into the Dense Forest alone.