Clara/Claire - [name_f]Clara[/name_f] feels like a good choice - a beautiful name, not too popular but familiar too
[name_f]Isabel[/name_f] - sleek and pretty, but [name_f]Isabella[/name_f] is popular, so she might still encounter others with similar names/nicknames if that worries you
Camila/Mila - both of these rank highly too (at least in the U.S for both, for [name_f]Mila[/name_f] in the UK) lovely names but you might encounter the same problem - I do like how [name_f]Mila[/name_f] and [name_u]Liam[/name_u] share letters and it is a nice name though
[name_u]June[/name_u] - charming and warm and unexpected
[name_f]Lucy[/name_f] - sweet but strong, familiar and in the top 100 but not super popular. A lovely name. [name_f]Lucille[/name_f] ‘Lucy’ or [name_f]Lucia[/name_f] ‘Lucy’ could be options
[name_f]Elle[/name_f] - short and simple and sweet, not my fave on your list, but I like it. [name_f]Annabelle[/name_f] ‘Elle’, [name_f]Elora[/name_f] ‘Elle’ came to mind
Marigold/Goldie - pretty, unexpected, vintage and clunky cute. I do like it 
[name_f]Rose[/name_f] - charming, simple, solid and sweet - a good option. [name_f]Rosemary[/name_f] or [name_f]Rosalie[/name_f] ‘Rose’ could be longer forms if you wanted them
[name_f]Lillian[/name_f] - a gorgeous name but a bit rhymey with [name_u]William[/name_u] for me.
[name_u]Ivy[/name_u] - depends where you are, but this is gaining popularity. Still, a bright, pretty name!
[name_f]Clara[/name_f], [name_f]Lucy[/name_f], [name_f]Rose[/name_f] and [name_f]Marigold[/name_f] stand out for me 
A few other ideas:
[name_f]Phoebe[/name_f]
[name_f]Beatrice[/name_f]
[name_f]Helena[/name_f]
[name_f]Natalie[/name_f]
[name_f]Josephine[/name_f]
[name_f]Eliza[/name_f]
[name_f]Naomi[/name_f]
[name_f]Arabella[/name_f]