Since you do not have digital deluxe Sims made in the game will not use items from that. The clothes that Sims that comes with a certain pack wears are included in the pack itself. Baby Ariel is special in two ways She does not age and she has no last name Baby Ariel is the first name Since you say you edited her in CAS you will have been prompted to enter a last name.
By the way here is a picture of her in her formal dress. It is a base game dress.
@jpkarlsenBaby Ariel’s dress is from Digital Deluxe. It is even shown (but in red) in one of the pictures in the link you sent.
Edit: Here's a screenshot from the page you linked @jpkarlsen. It's the same dress as the one Baby Ariel is wearing, and Kayla Flemming too.
Try doing a factory reset as described in this post: http://answers.ea.com/t5/The-Sims-4/FAQ-Troubleshooting-Steps-amp-Known-Issues/m-p/3621199
As I wrote earlier clothes used in a pack ships with that pack if they are not basegame items. Repairing the game should insure you have all the required items.
