You are correct that both Alaska and Idaho are members of the Drivers License Compact (DLC) so if you plead guilty and are convicted of speeding 24 mph over the speed limit in Idaho; Alaska's DMV will be informed of the conviction.
The Alaska Division of Motor Vehicles notes that if you are convicted of, or forfeit bail for, a moving traffic violation occurring in this, or any other State, points will be entered on your Alaska driving record.
Assigned points are based on the schedule which is listed in the Alaska Driver's Manual. Here it notes that for speeding 20 mph or more over limit it is 6 points. Keep in mind that accumulating 12 points in 12 months or 18 points in 24 months requires the mandatory suspension or revocation of the driving privilege, regardless of the hardships involved.
So it would appear that the ID speeding citation will be placed on your AK driver's license and be assigned points as well. To find out more about how the Alaska DMV deals with out of state violations contact the AK Division of Motor Vehicles through their website or at 1-907-269-5551.