Light aircraft instructor pilot reported a close encounter with a tower when he was heads-down working a checklist.

Narrative

Student and I were returning from a VFR day training flight when I went heads-down to work a checklist as he had forgotten to accomplish it. Looked up and realized we were both too low and headed straight at a tower that was 600 ft. MSL while we were at 1000 ft. MSL. I took immediate action to try to avoid violating the minimum safe altitude requirements; but I'm not sure if I was able to meet the separation requirements for the obstruction.Contributing factors to this situation were turbulence which caused me to spend a few extra seconds sorting out the checklist than it would normally take; new and unfamiliar avionics; and fatigue. Though the flight was early in the day; I tend to fly weeks of up to 35 hours of dual given and often find myself flying with less sleep than I would like. I also found myself spending too much time working with and configuring avionics that I was unfamiliar with instead of keeping a closer watch on our altitude.To prevent this issue again; I will take note to be more vigilant with the altitude coming in from the direction I was returning from; though the practice area we were returning from is used regularly; I am often vectored such that the tower in question would never be a concern. Additionally; I have spent additional time studying up on the avionics which had left me slightly distracted. As an instructor; I must continuously work to improve my performance in the airplane in regards to both flying it and simultaneously providing the best instruction I can to my learners.