There is a Preschool centre in Mt Eliza on Nepean Highway called: Guardian Early Learning Centre. There are also a lot of parks for children to play. What you can also do is have a look online at 'Whats on - Mt Eliza' and they may also have some activities for children happening.
There are a lot of attractions in Mornington for children and Mount Eliza's beaches are very enjoyable. In fact, Canadian Bay Beach is the ideal beach for young children given its incredibly shallow water and sand banks. Not to mention it is sheltered from the elements because of the nearby Canadian Bay Yacht Club. Mt Eliza's beaches area also commonly shaped like coves which make them protected and safe.