I'm not familiar with language immersion programs. Sounds very interesting.
I think testing is key if the school will use the results to provide a program paced to meet her needs. Otherwise you may find that even the LI program does not move fast enough for her. My DS7 loves learning Spanish yet hates his Spanish class bc of the constant repitition.
Also on testing - I would do both private & school testing. If the school will do a real IQ test like the WPPS-III I would start there. Beware - many school personnel conducting testing are not qualified and they may use a test that measures achievement not IQ. I work in schools as a consultant to child study teams and if parents saw & heard what I do - they would not rely soley on school professionals.
If you disagree with the school then the money spent on private testing may be well spent - unless you live in a state like NJ where schools do not have to accept outside testing. In NJ most schools will only test pre-K kids if they suspect or know of a disability.
Don't know if you have any Waldorf, Sudbury method, or Friends schools in your area but you may want to look into them. Especially Sudbury method schools. We have none near us so we are planning on sending DS7 to a Friends school and forgoing any retirement plans. :-)