To clarify, this issue won't be able to be resolved for Children's Week this year. If you completed the quest previously you won't be able to complete it again for the other pet this year.
This is sad news, indeed.
[T]his is an issue we are presently looking into. At this time, players who completed the Dalaran Children's Week quests will be unable to re-accept the quests. We hope to resolve this issue as soon as possible, but we do not have an ETA to provide at this time.
We will surely let you know as soon are more information becomes available.
And of course, we at WarcraftPets will do the same. We're hopeful that Blizzard will have this bug fixed before the event ends. It's logical to assume it will be addressed during Tuesday's maintenance. So enjoy the other CW quests and sit tight... more likely than not, a solution is coming.