C172 Flight Instructor reported landing safely after experiencing loss of power and low oil pressure on final approach.

Narrative

I was flying with my student at the ZZZ airport and we were practicing a Power-off 180 maneuver to prepare him for his commercial pilot practical exam. Upon pulling the power to idle; I noticed that I was able to see the propeller disc in front of me. After a few seconds; I glanced down and realized that the oil pressure had dropped to below operating minimums. I instructed the student to add power and that brought our oil pressure back to within the operating range. I then took control of the aircraft and performed a landing with full flaps and about 1/2' open on the throttle. Landing with this throttle setting produced a little bit of a bounce as I was unable to effectively bleed off energy in the round out and flare. Upon slowing down to a reasonable speed; I was able to exit RWY XX at 1 and I contacted ground while rolling to prevent an engine failure on the taxi way. Upon leaving the airport movement area; I moved my mixture to the full rich position and I pulled the power to idle; the engine died within a few seconds. My student and I were able to coast back to the tie down spots and we shut everything down and immediately called an A&P to come inspect the aircraft.Upon reflecting on this incident in the aftermath; I should have declared an emergency on short final and communicated my problem with ATC as soon as I was on the ground. I was hesitant to do so because I knew that there was traffic behind us in the pattern. In the future; I plan on monitoring my engine vitals more effectively as well as taking preventative action faster.