Is it possible to copy the data from this on to a blank fob and could a professional locksmith such as Lock Doctor do it ?
It's a Paxton Net 2 proximity sensor.
These are much more complex than say old gate fobs that just send the same signal/frequency each time and can be easily copied.
It looks like you might have a shot at cloning one if you were willing to buy some hardware and hope the password on the system you’re trying to access has not been changed, but it’s far from easy - https://forum.dangerousthings.com/t/cloning-hitag2-pcf7936/12086/10. Not sure how deep Lock Doctor are willing to go with something like this, my guess would be not deep enough though!
Can you not have a new fob added to the system legitimately instead of cloning one?