Goitre, apparently.
“He said goitre was so prevalent in Tasmania that the State Government provided daily potassium iodine tablets to schoolchildren in 1949, but the program was eventually dropped as it wasn’t an effective measure during school holidays.”
https://www.abc.net.au/news/2019-06-13/curious-hobart-origin-of-two-headed-tasmanian-myth/11197982