6.9 miles, Full day
The hike from Mineral King to Eagle is short and steep with about 2200ft elevation gain in 3.4 miles. The hike starts at an elevation of about 7600+ and reaches just below 10000ft at Eagle lake.
This is a moderately difficult hike and can be finished in half a day, although it might be more relaxing if you have a full day.
The 25 mile long road to Mineral King Valley from Three Rivers takes about 90 minutes to drive. So if you are planning to come in hike and get out of the valley, plan accordingly.
Acclimatization at high altitude will definitely help since the hike reaches about 10000ft at Eagle Lake.
This seemed to be a popular day hike in the area and you will find a lot of hikers during the weekend.
Talk to a ranger about the marmot problem during spring and early summer.