The subject of this article or section is part of Children's Week, a seasonal event that lasts one week. Once the event has run its course, this will no longer be available until next year, but there are no guarantees.
The other two item reward options from the quest line are Sleepy Willy and Egbert's Egg. Only one of these can be chosen per year, but when the event repeats itself next year you will be able to choose another.
You'll notice that baby elekks have ear flaps, though it is thought that the ears change into horns when the elekk reaches adulthood. Speaking in evolutionary terms on the survival of the species, this doesn't make a lot of sense, but Blizzard's logic rules.