Electric Iron

It's small and heavy, and I imagine it got pretty hot (though I wouldn't plug this one in, considering the condition of the cord). It's 5 inches long, and the stand plate on the back reads:

Volts 110, Wt. 1.5 lb
Lady Dover
Dover Mfg Co. Dover O U.S.A.

Perhaps this is a travel iron, or perhaps in the past people trusted their kids not to burn themselves.