This drink is much more recent than you may think. Unbelievably, there is no purported history of this drink, it seems odd that such a classic would be so unresearched. Here is an early printing of the drink:
LIFE - Dec 24, 1951 - Page 25 Vol. 31, No. 26
"Hot Buttered Rum: Combine 1 tsp. brown sugar, 2 cloves, M tsp. allspice, 2 oz. rum. Add half pat butter, and then fill mug or glass with boiling water; cinnamon stick. 4. Flip: 1 whole egg, 1 tsp. sugar, 2 oz. of rum."
The drink actually appears as early as:
The Kenneth Roberts reader by Kenneth Lewis Roberts in 1945
"Hot Buttered Rum"
No recipe is given though. The drink has no location associated with it. The ingredients in this drink could easily decieve someone into thinking it is a vintage cocktail, which is a great explanation of why many believe this drink is age old.
There were several advertisements for this drink made by Myer's as seen in these publications:
LIFE - Sep 21, 1942 - Page 24
LIFE - Nov 30, 1942 - Page 129 Vol. 13, No. 22
This drink was very likely created by Myer's and dates between 1940 - 1944 and contained at least as of then:
Build these ingredients in an irish coffee glass or other heat retaining vessel:
Myer's Dark Rum
Garnish with a Cinnamon Stick