I would draft a letter you'd like the allergist to sign and then ask allergist to sign it. In my experience, having the allergist (office) write the letter is not always as thorough or direct to the issue. When asking the allergist to sign, always offer that the allergist may suggest necessary changes and then you negotiate and get to something the allergist will sign.
If this is child who already has 504 for LTFA and/or asthma, then this might be separate section on the 504 as it does potentially affect the ana reax situation in some cases.
Whatever I do, I would NOT give the school carte blanche to access the physician.
And the allergist's letter should not say in closing, "Please call my office with any questions" as you are not authorizing that, right?
If child has no IEP or 504 for anything else, then there would need to be at minimum an IHCP (Health Care Plan) developed to address . . . and again, that will take letter from doctor (don't need test results, can be general in detail but state specifically the animal(s) allergic to and the potential for adverse affects on patient).
Now, doctor might wish to do new allergy testing to re-confirm the animals allergic to . . . I'd be willing to agree to that, but in meantime there must be a letter from doc and a plan at school to address the immediate situation. I'd think if there was old positive SPT and now this new history of reactions and problems in the rodent classroom, then that would be enough for doc to sign up to accommodations and some changes, yes?
Sounds like a 2-prong approach -- what to do ASAP and then get the documentation and testing done to have something on record for longer term (likely just the rest of school year & would re do for next year).
Does that help?