Our DD was very similar in her nature so I understand your concerns. Fortunately our experience with acceleration was very positive so I wouldn't rule it out particularly if you change school districts and leaving friends is going to happen regardless. If you or she have concerns then SSA with an opt out clause might work as a trial. If her third grade class is going to be doing something fun then maybe she can do that and go up for maths at other times.
Your other option is differentiated work in the classroom and allowing her to do higher grade material. We found a few challenges with that option. Our DD likes to work and learn with others so even though she works well alone it isn't as much fun for her. It can also be hard if the third grade teacher doesn't fully support it or lacks the time to provide adequate instruction.
The other issue is that it sounds like your daughter is not just bored in math. Maybe yo can explore all possible options with the school before you consider moving. A flexible school that is willing to work with you is often hard to find and can be more valuable than one touting GT options. Flexibility is key with our kids.
