Yes, it's a good find. Walters was a family which made their fortune initially in liquor dealing and retailing (not distilling). Later, it branched into railroad and financial investments. Baker was one of the reputed brands it sold in the mid-1800's, it was Pennsylvania rye, a classic type of rye whiskey, country cousin to bourbon. Rye whiskey is still sold but none is made currently in Pennsylvania, or in Maryland where the Walters had their first business.
When the heiress and descendant Mrs. Walters died in the 1940's, her estate sold the collection of fine spirits remaining after the liquor business had long ceased, or which had been acquired on the way by her ascendants. It included wines, brandies and many other spirits, but also some of the rye whiskey which had helped to make the family's name and fortune. Foremost among those was Baker's rye.
That 1840's Baker's would date to the early years of American straight whiskey production.
If it was mine, I'd open it and taste it alongside a current rye whiskey, say Michter's 10 year old rye, and see which is better. Then re-stop it with a stopper cork, the one from Michter's rye would probably be fine, or use any wine cork.
Indeed the Walters Museum is going strong and houses the fine art collection which the family had amassed.
P.S. My information is from a Walters family history which you can buy at the museum.