Looks like a self blue to me. She's probably a bantam cochin if she is staying small. They lay small eggs 3-5 days per week. They are a very docile breed and are some of the best pets. I own two and am working on getting a breeding rooster.
Yes she is staying small. Those are her baby pictures. She has laid her first egg now. She got very territorial when I added a new chicken as a playmate but now they are super friendly. One isn't seen without the other