My daughter has severe allergies to milk, fish, and peanut. Her allergist thinks she's a good candidate for peanut desensitization. Is this safe?

Possible. Peanut desensitization is an emerging option for pt with peanut allergy. However, this is still in the investigational stage and not all patient are candidates. If one is interested in this treatment option, i would strongly encourage speaking with an academic center that is actively researching this area.