The etymology of Donut

When my young daughter said or did something worthy of the name, I would call her a silly sausage, as an innocuous, playful tease.  So when my son became old enough, (he was born in 2000), I used the same phrase.  But he objected to it, not wanting to be called a sausage.  Not wanting to upset him, I tried to think of another fun, food related play-name.  We all like donuts, so I picked that and he seemed to prefer it.  If he spilled his drink, or teased his sister, or made a joke, I'd call him a donut.

He and I even came up with a silly song together:

You're a donut, you're a donut,

you'd be doing quite well if you had a brain cell,

you're a donut, you're a donut...

I'd never heard the term used in that context before, but it was picked up by other family members.  We travelled the UK, from the south coast of England to Scotland, through cities and theme parks, and never thought once of the influence we may be having on our language as we may have been overheard.

A few years ago I heard Al Murray use the expression on TV, and wondered where he heard it.  Then last week, I heard it on Eastenders too.  I mentioned it to my son, who looked up the origin.  He found a couple of sources, not before the early 2000s, one in Scotland and one in southern England.

So I'm wondering, did I coin the term donut, as a playful name for a silly person?