I wonder if this will reach you nearly 4 years after this post. The school you are referring to would have been Tintern Girls School which was on the east side of Glenferrie Road just south of Oxley road. The school was established in 1877. It moved to Ringwood in 1953. The site is now occupied by the Hawthorn library and Community centre.
Hawthorn Historical Society is only too happy to answer any historical questions about the area (if we can). We have a website and are on Facebook too. Elizabeth Yewers