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.
Here you can see what is in Digital Deluxe.
http://simcitizens.com/the-sims-4-digital-deluxe-edition-content-overview/
