How do I determine whether the existing fixture can support a ceiling fan?
You'll have to look at the inside of the box where the light is mounted. It should have printing inside it - although at the age of the house, it may not. Boxes that can support ceiling fans will be known as "acceptable for fan support":



If you don't see something like that, you're going to need to take out some of the ceiling and replace to box with a fan box or run the risk of the fan being too heavy and falling down at the worst possible time.