I haven't posted here in a long time but wanted to add another vote for moving to Level 5. My dd competed last year as a young 6yo Level 4. In fact, she did not turn 7 until this past Fall. She did reasonably well at Level 4, but the coaches were on the fence about her competing Level 5 due to her age and her small size. Like you, I asked her what she wanted to do and I explained to her that she might not score very well at Level 5. Like your dd, she told me she wanted to do Level 5. She was adamant about not repeating Level 4. We are now mid-way through her Level 5 season and she is struggling on bars and vault, but she has all her skills. The kip is still not perfect and she is just now consistently getting over the vault, but it's starting to come together and her scores are coming up. She has, in actuality, gotten a couple of medals this year, though certainly not anything approaching first! More important, the lack of medals does not bother her. She's happy training Level 5 and even getting to learn some Level 6 skills. We started this year assuming she would repeat Level 5 and that may still happen, but she will train Level 6 over the summer and if she gets her skills she will move up.
All this is to say that your dd may struggle a bit in Level 5, but if she really wants it and she understands that she may not score well, then I would let her move on. I am happy I did, but I also knew that my dd is not a child to worry about how she places. She wants to score higher for herself and she wants to qualify to State, but what place she gets isn't a big deal. If your dd is the same, she will be fine in Level 5. I also totally agree that Level 5 is the level to repeat, not 4. She will be working on skills like the vault, kip, squat on and jump to high bar, that she will need for many more levels to come. And just think - you'll never have to worry about that mill circle again!
Meg