First, welcome to the forum.
Your concern is entirely justified. Avoiding over-night hypos is an essential part of managing things if you are a type 1 diabetic. General practitioners tend to know precious little about living with type 1. May I ask how long ago you were diagnosed and do you attend a hospital clinic ? Do you have access to a DSN ?
Edited to add - Sorry, tim2000s - you beat me to it. I agree that a DSN is the best person to help in this situation. I had missed the fact that Jenny1974 has been diagnosed for 34 years. Sorry, Jenny.