0.34A is the average draw. The peak draw on the transponder is greater than 1A, so a 1A breaker is not sufficient. It will blow at some time in flight.
The transponder is a certified device and must be installed per the manual. A 3A or 5A breaker or fuse must be used. 3A is the minimum to deal with the peak loads, 5A is the max to deal with the rating for D-sub pins.
Remember, breakers protect wires, not devices. As long as all the power wires in your plane are AWG22 or greater, you could wire the whole plane with 5A breakers per AC 43.13-1B and you would be protected.