I don't think a 504 is designed for the behavioral/emotional issue you face, and an IEP would be required to provide any protection - say against expulsion on behavior grounds. A 504 is more for accommodations like a ramp where walking was an issue, or certain assistive devices etc. The question is really whether or not your daughter's behavioral issue (a) is in a category listed in the relevant law (IDEA), and (b) has a significant adverse impact on her learning.
There is a lot more to it, but jal is right that a letter to the new school's director of special education - or to the principal of the school she will attend - is the way to start the process. Elsewhere on this site are sample letters. Certified mail will provide proof of delivery at less cost than registered mail. Do note that your daughter will have to be available to the school representatives/evaluators for them to do anything, so timelines wouldn't start until she was so available - and you had provided proper written authorization.
In terms of immediate protection, there seems to me little or no value in sending (or hand delivering, the method I prefer) the letter before she enrolls in the new school.