The proper name of this page, Can I Keep It?, contains a question mark which gives the wiki trouble. Therefore the Wikibase title has had the question mark removed.
There seems to be a hidden timer to this quest. If you do not take the pup back to camp in a timely manner Handler Shirsha loses interest in him and the pup cannot be dismissed. Camping out and back in will not dismiss him but does renew Shirsha's interest in him!