A 9V motor will "look after itself" when operated from 9V in normal operation. If stalled it may draw excessive current. A slow blow fuse in the motor circuit will minimise the risk of damage under overload conditions.
If you have a "proper" plug/socket on the battery connection it would be common to have no protection in the battery pack. shorting 6 x D cells in series can cause a fire so a slow-blow fuse in the pack itself would not be a bad idea but in a one only situation it's up to your personal risk aversion and carelessness factors whether you use one. If this was for a high volume consumer application then a fuse would probably be required to avoid potential liability issues.
You have a potential technical problem with your proposed solution. 6 x D cells will produce about 9 volt when new (Alkaline, Zinc, "Heavy dury", ...) or about 8 Volt for NimH or NiCd. BUT as they discharge the voltage will drop, rapidly at firs and then more slowly, to about 1 Volt per cell when nearly fully discharged. A non rechargeable cell will spend a lot of its life in the 1.1 to 1.3 Volt range or say 6.6V to 8V output. Your motor may work PK at these lower voltage or may work badly or not at all depending on the application. You need to try the motor at lowest battery voltage (about 6 Volts or even less loaded) and see if it works acceptably.