PC-12 pilot reported they switched NAV sources which caused the auto pilot to disconnect resulting in the aircraft descending too low on the approach and a Ground Proximity Warning along with an ATC Low Altitude Alert.

Narrative

I had been cleared for the ILS XX approach at ZZZ and directed to maintain 3;000 ft. until established. I was in VMC conditions with a broken layer well below my altitude. I was vectored to the final approach course and intercepted it utilizing GPS. Outside the FAF; I attempted to switch NAV sources from GPS to LOC. I believed I had set the NAV 1 radio to VLOC. I later discovered that I had selected VLOC in the NAV 2 radio which was why I was unable to find a LOC 1 setting in my NAV source menu.Switching NAV sources caused the autopilot to disconnect. When I was unable to locate a 'LOC 1' in my NAV source menu; I became distracted by that issue and did not notice that the aircraft had entered a descent. When I did notice the descent; I incorrectly believed I was inside the FAF. Approximately ½ mile outside the FAF; I received a GPWS altitude alert. I responded to the alert by adding power and initiating a climb. Simultaneously; ATC issued a low altitude alert. I advised ATC that I was climbing and requested vectors for another approach. All of this occurred in VMC conditions above a low broken/scattered layer. The subsequent approach was completed without incident through a thin low broken/scattered cloud layer.Learning points. I will ensure that I closely monitor which radio I have configured for the approach. When the autopilot is engaged; I will ensure that I temporarily select HDG mode when changing NAV sources. When I had trouble with the NAV source selection; I should have reengaged the autopilot in HDG and ALT mode while I troubleshot the issue. If the issue could not be troubleshot in a timely manner; it would have been appropriate to request vectors for another approach; this would have provided additional time to identify the issue.While I regret that this incident occurred; I am thankful for my training which enabled me to immediately; and appropriately; respond to the GPWS message. In addition; I am appreciative of the alert ATC Controller who issued the low altitude alert. I am committed to lifetime learning and view this incident as a significant event that will help me be a more proficient pilot. I also plan to share with other pilots so that they may benefit from my learning experience.