Hi there.
I’m more of a fancier full name cutesy nick-name person myself. But based on your list, I’m guessing that you just want the full name to be the name that she goes by. That being said, I’ll give my thoughts on the list based on that mentality. 
Sunny-It’s cute, but I don’t know. It’s just a little too cute for me.
Sally-This one seems more established. It’s sweet & friendly like [name_u]Sunny[/name_u], but it’s also a little homier & not too bright, you know? Plus, it’s old fashioned yet not heard terribly often.
Betty-I don’t mind this that much on its own. I still prefer it as a nn, but it’s somewhat more established as a full name than some of the others. It’s cute. Classic & light. Simple, but not too over used.
Dolly-I kind of see this one as too cutesy as well. It’s what little kids call their baby dolls. [name_m]Just[/name_m] a little childish sounding for a full name.
Indie-I can’t get into this one, even though I’m loving [name_u]Indigo[/name_u] recently. It sounds a little too not like a name.
Nellie-[name_u]Love[/name_u] it! I love this so much that I’m probably willing to break my personal don’t use a nn for a full name rule. It’s just the perfect balance of smart & bookish, with friendly, sweet, girly & vintage.
Daisy-
The top name on my personal list. It has such beautiful flower imagery. It’s vintage, charming, happy & lovable. I have no good explanation as to why I am okay w/this as a full name & not [name_f]Dolly[/name_f] or [name_u]Sunny[/name_u]. It just maybe seems like its been used on its own more historically?
Drew-Meh, I’m not into this one. I feel like w/a little sister after two boys, I’d personally pick something obviously feminine. And [name_u]Drew[/name_u] is just really popular for boys.
Sasha-This is a name that’s unisex as well, but you don’t hear it a lot for either sex. So, it doesn’t seem as off-putting on a girl as [name_u]Drew[/name_u] does to me. I kind of like it. It’s unique, simple & spunky.
Kit-It does seem really short on its own, but I love how sweet yet sporty it is. Reminds me of the endearing character in A League of Their Own.
Here are a few more ideas that you may like:
Audrey
Alice
Bess
Clover
Cate
Flora
Greta
Hattie
Ivy
Juno
Lucy
Lilie
Molly
Maisy
Olive
Phoebe
Polly
Posy
Ruby
Sadie
Scout
Tess
Thea
Violet
Wynn
Hope this helps. 