The Harry Potter fandom: taking the fun out of writing fanfiction since 2000.

It's true if you're just reading from the books and not using any of the information that comes out in chats that there is no reason to believe that Minerva is in her 70s. There's no information in canon itself that indicates that wizards live longer than Muggles.

Keep on doing what you're doing; if you're enjoying the writing, that's all that matters.