There is only one school in Exmouth, which services Kindergarten to Year 12 (K-12) - Exmouth District High School
https://www.det.wa.edu.au/schoolsonline/overview.do?schoolID=4077
http://exmouthdhs.wa.edu.au/
There is also a TAFE for those who wish to pursue further education:
https://www.centralregionaltafe.wa.edu.au/campuses/exmouth