Doctor Ironheart was my favourite song that I learned at school in Australia.
It sounds like an adaption of Dr. Iron Beard / Doktor Eisenbart.
Here are the words as I remember them.
If anyone has the correct wording please let me know.

For I am Doctor Ironheart. Fal-a-didle-ay ho ho
I heal the folk with curious art. Fal-a-didle-ay ho ho
For if you come what ever your pain Fal-a-didle-ay ha ha ho ho
You'll never need return again Fal-a-didle-ay ho ho

There was a man from London town. Fal-a-didle-ay ho ho
Who had no wits beneath his crown. Fal-a-didle-ay ho ho
He asked me to improve his head. Fal-a-didle-ay ha ha ho ho
I used an axe and now he's dead. Fal-a-didle-ay ho ho.

An aching tooth a swollen cheek. Fal-a-didle-ay ho ho.
A man brought me relief to seek. Fal-a-didle-ay ho ho.
With a pistol ball his tooth I shot, Fal-a-didle-ay ha ha ho ho.
And no more aches that man has got! Fal-a-didle-ay ho ho.

To sleep the patient tried in vain Fal-a-didle-ay ho ho.
For in his neck he felt great pain Fal-a-didle-ay ho ho.
I tied a noose and pulled it tight, Fal-a-didle-ay ha ha ho ho.
And now he sleeps both day and night Fal-a-didle-ay ho ho.

Good friends you thus will clearly see Fal-a-didle-ay ho ho.
How quick and cheap each remedy Fal-a-didle-ay ho ho.
For if you come whatever your pain Fal-a-didle-ay ha ha ho ho.
You'll never need return again Fal-a-didle-ay ho ho.