You don't need "by" because of the word "prior". It acts like a preposition. There is a slight difference in meaning using "by" and "prior". In using "by", it means you can have up to the last day to pay before you leave. "prior" means that you must pay earlier than the last day. "prior" = "before" "by" = "until"

"By" isn't needed here, but it is true that "by" is often used with "due" -- especially when saying that something is due at or before the end of some time period, or at or before some action. You might say the money is due BY the end of the week. Or BY the moment of departure. Or BY the time that you leave. It would be incorrect to say "the balance of payment is due the time of departure." You would need "by" in a case like that.

It is correct the way it is. Putting by before one month wouldn't make a lot of sense.