I too worried about daycare's recommendations if they don't believe she is gifted. Is this straight daycare or is there a preschool component/program? I ask because I wonder how much opportunity your daughter would have to show her giftedness in a play based daycare? We had the opposite experience in that the day care teacher picked up on our DD's giftedness. They had an incorporated preschool program so more opportunity to demonstrate her academic side.
Rereading your post, the main concerns seem to be:
1. You are not sure whether the test result is accurate
2. The social aspect and friendship groupings
3. Not having care if the early entry doesn't work and you worry it may not because of 1 and 2.
While I have always been told it is possible to underscore rather than over score in intelligence testing, your DD is very young and there is a question of score stability with early testing. Still, I am sure, as Puffin pointed out, that there were reasons you tested so she must be showing exceptionality in some way.
The social aspect worries all of us. No one wants their child alone at school. The problem is that finding friendships and peers is really hard to predict and depends on so many factors. There may be great friendships to be had next year but it's hard to know. No guarantee about the year after though as age is not the only factor.
Is she going to be ready for school in all other ways, toileting, managing clothing, coping without excessive fatigue etc? School can be quite tiring as there are more demands on the child's executive functioning and, hopefully, with the intellectual stimulation. These are things to note as the year goes on.
I would put in the application but reserve judgement until much closer to the day while continuing to assess your daughter's development.
