I associate this word with mice in clean petticoats, but that's probably something to do with an early over-exposure to the works of Beatrix Potter (her little books were cheap enough to be Sunday School prizes, and at one time that was the main way I got hold of books).
Dimity is a beautiful word, prim-yet-energetic, and it's always been a favourite. You can hear it skipping as it goes. I suspect this is why, especially in Australia, it's been used as a girls' name.
Dimity is a strong cotton fabric, usually white (though it can have stripy patterns) with some thicker threads woven through it. Nowadays it's most usually used for upholstering beds or making curtains.
In former times dimity was used to make bustles, so my mice-in-petticoats idea isn't too far out:
Sadly for its wholesome image, a dimity also used to be a sort of almost-invisible upper garment worn by early and shy exponents of the strip-tease.
Which is still rather sweet, when you come to think about it.
Word To Use Today: dimity. This word comes from the Mediaeval Latin dimitum, from the Greek dimiton, from mitos, warp thread.