Here are some starting places. Looks for shows that Julie Andrews has performed in the past. Those songs will be of similar style and vocal range many times. These include: My Fair Lady, Cinderella and Camelot. Lots of great soprano songs to work from there. Mary's songs definitely show a lot of range in Mary Poppins.
Also think about other movies that the Sherman brothers composed songs for: Chitty Chitty Bang Bang, Bedknobs and Broomsticks and The Jungle Book. They might not all be "traditional" female songs but they reflect a similar writing style. Hush-a-bye mountain from Chitty Chitty is lovely..and Mary sings a similar song or Doll on a Box. The Bare Necessities from Jungle Book, The Age of Not Believing from Bedknobs.
If you don't know these songs, you can listen on iTunes and get the sheet music (where you can easily adjust the key) on musicnotes.com.