To be preoccupied with something means that you are thinking about it and it's difficult for you to think about other things. Since this usually happens when you don't want it to happen, it's unusual to predict it will happen in the future, and it isn't normally something you decide will happen in the future.
I think you want to say, for example "I have some personal work I need to do on that day" or "I am planning to do some personal work on that day" or "I will be occupied with some personal work on that day".
However, as pointed out by oerkelens in a comment the sentence isn't grammatically wrong. "I'll be preoccupied" "I'm going to be preoccupied" and so on are correct. They just don't express what you mean.