You know, she is only 3 years old. At this age, having her write letters is a difficult task that can cause frustration because of small muscle maturity. If any writing of letters is done, it should be writing her name using a capital letter to start, followed by lower case letters. Coloring, Playdough use, Leggos, etc. will better develop small muscles and be much more enjoyable. The daycare provider could help her learn the letter names through books, block play (with letters on them, games, etc. (far more age appropriate).
Of course, it would be more enjoyable for her to have playmates her own age at the daycare, but not a neccessity. I think a 1/2 day 4 year old program next year (even only 3 days) would be good for her and give her an understanding of what will be expected in Kindergarten (listening and following directions in a large group, taking turns, sharing, lining up to go to the bathroom, lunch area, etc.)
Good luck...