There are some great schooling options in Mornington!
Mornington Secondary is the only public high school in Mornington itself. It has great facilities such as its large basketball centre and an indoor swimming pool. Also in Mornington is Padua. However, it isn't a public school but its worth mentioning as the fees aren't huge and its seen as great value by many. Outside of Mornington there is the likes of schools such as Mount Eliza High which has become a very highly regarded school.
For primary there is many options, of which they are all great schools. In Mornington, you have Mornington Primary School, Mornington Park Primary school and Benton Junior college. However, Mount Eliza also offers some great primary schools such as Mount Eliza Primary, Mount Eliza North Primary and Kunyung Primary. You can't go wrong with any of these options, I'd recommend going with whatever is closest and/or has the best feeling for you and your children.