my devoted head
Johnson's 1755 Dictionary offers us the appropriate definitions for this period, definitions virtually lost to modern English usage:
To addict; to give up to ill.
To curse; to execrate; to doom to destruction.
For the second meaning Johnson helpfully cites the Satanic legions in Paradise Lost, V.890.
The phrase "devoted head" is so common a usage as to appear to be a customary eighteenth-century idiom.