Is it permissible to delay prayer due to a nocturnal emission after Fajr prayer and going to school, which leads to missing Dhuhr prayer?

It is not permissible to delay the Dhuhr prayer beyond its time while waiting to purify oneself. Rather, one must perform ghusl at home before going to school if possible. If the time for prayer arrives and you are unable to perform ghusl at home, then you must search for a place to purify yourself. If, after searching, you cannot find such a place, and you will not return until after the Dhuhr time has passed, then you must perform tayammum with the intention of removing janabah and perform the prayer within its prescribed time.