Hi,
Our school is a little anti-acceleration as there are so many bright kids, it feels as if they let one person move others will want there kids to move too... But it should be based on need rather than iq right? I wouldn't be asking if DD was fine and happy.
I think the reality is likely that there are many bright kids at your school and that if one child is moved, other parents will use that as a point in advocating to move their children up - so from that perspective, I understand the school's point of view. OTOH - I think that you can use that to bolster your advocacy for more challenge - because if there are other bright kids who are also having the same issue your dd is, then the school can't argue that "we can't make an exception for just one child". It could all turn into a circular conversation - who knows if you'd end up with the grade skip or with differentiated ability grouping at a new level where your dd is at - but in either case, it's the kind of discussion where if the school says they can't because of numbers... you can argue that having the numbers allows them too... then in return if they counter that your dd is still outside "the numbers" that supports your advocacy for a grade skip or other individualized solution for your dd specifically.
Re what else can you do to show your dd is more capable - we were stuck during much of elementary school without meaningful differentiation or acceleration - but while we were in that "stuck" zone we had our ds work on things he was passionate about and strong in at home, and we kept records showing what he did at home that could be used to advocate later on - and we successfully advocated for an appropriate grade skip in math when he entered middle school. I'm not suggesting you wait until middle school - you definitely should be advocating now and if anything I wish I could go back in time and be a stronger advocate for my ds - but - keeping a record of the work she does at home, and perhaps purposefully having her do some work that you can have to put into a portfolio showcasing her abilities can be very helpful. Also having a good set of data from ability and achievement tests in your back pocket to bring up when advocating. Granted, the school should know what her results are, but it has been helpful to us to have actual copies on hand when we are at school meetings. Just in case the school forgets

Best wishes,
polarbear