If you're not sure about Millie but think you might come back to it then I agree with PPs that it would be an idea to go for one of the (many) names that could easily abbreviate to Millie.
Alternatively, names that I think have a similar vibe to Millie:
Annie, Abbie, Avery, Bonnie, Betsy, Betty, Connie, Callie, Cassie, Carrie, Casey, Daisy, Darcey, Dulcie, Elodie, Ellie, Evie, Elsie, Esme, Edie, Frankie, Gracie, Georgie, Halle, Holly, Heidi, Hebe, Ivy, Indie, Jessie, Josie, Jodie, Katie, Kitty, Lily, Lucy, Leonie, Lexie, Lacey, Libby, Lottie, Misty, Molly, Miley, Macey, Marnie, Melody, Nancy, Nellie, Poppy, Polly, Penny, Ruby, Rosie, Romy, Remi, Riley, Sophie, Sadie, Sydney, Tilly, Tessie, Tammy, Vivi, Winnie, Zoe