The story
Possibly from dodder (“to shake or tremble as one moves, especially as of old age”) + -ard. The Scottish National Dictionary, a Scots dictionary, defining doddard as “A foolish old man, a dotard”, and providing an 1823 quotation, gives the etymology as either a variant of dotard, comparing Early Modern English dodart, or perhaps related to doddered, with spelling influenced by dotard.
Etymology from Wiktionary, CC BY-SA 4.0.