The William Shatner celebrity doll depicts him as Captain James T. Kirk  in the original Star Trek television series.  The show ran from 1966-1969 on NBC.

This Capt. Kirk doll was made by Playmate, Inc. in  1996 as part of the Collector Series, Starfleet Edition. The doll’s outfit is the standard issue Captain’s  Starfleet uniform and accessories include Starfleet communicator, Starfleet Phaser,  Starfleet Tricorder, and  Starfleet Delta doll stand.  Included is an exclusive space cap trading card.  This collector’s series was made to  commemorate the 30th anniversary of the show.

Other Star Trek action figures in the collection include:  Mr. Spock (Leonard Nimoy), Lieutenant Hikaru Sulu (George Takei), Lieutenant Uhura (Nichelle Nichols), and Captain Jean-Luc Picard from The Next Generation (Patrick Stewart).

Price check the William Shatner doll on Amazon

Price check the William Shatner doll on Ebay
 
 

 While not in the museum  Quantum Mechanix makes at least five high-end 1/6 scale action figures of Star Trek characters including William Shatner..