Yes you do and you can do so online. You do not need to prepay and they will sms confirmation to you as well.
I believe if you wish to go on a Sunday then you definitely need to book. They have two sessions one from 12 pm to 2 pm and then 3 pm to 5 pm.
I believe it would be better to pre book rather than just arrive and be disappointed.
During the week, I imagine there may be free tables but not the range of food that is available at weekends.
Get quick answers from Afternoon Tea - The Windsor Melbourne staff and past visitors.