OP, we were in the same situation last year. DD is currently in year 1, and is a June birthday. Like your dd, she is very bright and she is also a confident little girl. At the end of reception, her teacher said that they wanted to move her up a year and put her straight into year 2. I refused, instinctively feeling that it was better for her to stay with her peers. However, I did have some doubts about my decision later, particularly as some friends felt that I was mad to turn down this opportunity.
Fortunately, lots of lovely MNers assured me that I had done the right thing, and I concluded that I had made the right decision. However, I was still quite concerned about what might happen if I refused and then found that dd was getting bored in school - I was worried that they'd throw my decision back at me and tell me that it was my fault.
One year on, I couldn't be happier about the decision that we made. Her year 1 teacher has gone to great lengths to ensure that work is appropriately differentiated, and she continues to be happy and stimulated in school. Socially, she has forged strong friendships with the other children in her class, and I am so happy that we didn't separate her from her peers.
I think it's important to realise that children who are ahead in some areas may not be ahead in all areas. For example, my dd may be working several years ahead of her peers with regard to literacy and numeracy etc, she is very musical, and she also has extremely good social skills. However, emotionally, she is still only five, and she is also distinctly average at P.E. and art - she would be distinctly below average in a class of chilren much older than her.
If your dd is exceptionally bright, chances are, moving her up a year still wouldn't be enough because she will still be further ahead of her classmates. So the work will still need to be differentiated in any case.
At the end of the day, only you know what's best for your own child, and if your daughter is showing signs of boredom in school, I think that's cause for concern. However, if I were in your position, I would be looking for other ways of dealing with this, rather than moving her away from her peers. It is possible for a teacher to cater for a bright child within their normal class - I know because it's working for my dd. I hope that you can find the right solution for your child, and that the school is prepared to support you in whatever you think is the best approach.