According to all the sources I've read, the Kearsarge was in the yards from June of 1950 to February of 1952 for her SCB27A modernization. She did sea trials in the Atlantic and was sent to WestPac in the summer of 1952. Her Korean deployment went from September 52 through February of 53.
Her aircraft complements after the refit were of F9F Panthers, AD1 Skyraiders, F4U-5 Corsairs, F2 Banshee, and Dragonfly helo.
Before 1950, she would have had the F9F Panther, Corsair, M-1 Mauler, F7F Tigercat, and TBM Avenger.
Floating Drydock had plans for the Kearsarge years ago but no longer carry them. As far as pictures, there are few on the net of her in her early configurations so hopefully some vets or researchers here might have some better sources.
What period are you planning on doing this build? In 1/350, converting either the Trumpy Essex or scratchbuilding is going to be quite a job. Besides a redesigned island and wider hull, there is the question to answer as to where all the gun placements went and other small details since each ship was different. I know because I'm doing this sort of project also in both 1/350 and 1/700 of the Oriskany. Fortunatly, there is a lot of pictures of this more known ship.
White Ensign Models and Pacific Front Hobbies carry a range of aircraft for this period in both 1/700 and 1/350. However, only the Panther, by Corsair Armada, so far has been produced in the 1/350 jet catagory. All of the prop planes can be found in resin at these places. The Dragonfly helo also has not yet been produced in 1/350.
Another hint to find out about colors and details of these carriers in this time period is to watch two movies. "The Bridges at Toko Ri" and the "Cain Mutiny" both show extensive color and detail of a ship during the 1950 - 1953 time frame.
Scott