Locked away in a tower most of her life and guarded by a monster called Songbird, Elizabeth is rescued by Booker DeWitt. Her years spent locked up gave her a childlike personality.
Ref image. 1. Scene. 2. Outfit. 3. Eyes
If you need to see her outfit better here's a link. http://i1066.photobucket.com/albums/u413/xpockykillerx/BioShock-Infinite-Art-By-Alex-Garner-600x616.jpg