There's nothing woolly about "wally" (Scots)

Just watched the latest episode of "The Antiques Roadshow" on BBC1, which was filmed in Scotland. One man brought along a pair of "wally dugs" - flat backed china or porcelain dogs designed in pairs to sit at either end of mantelpiece, and often made in Staffordshire, though some come from Scotland. The English porcelain expert reviewing them had clearly never heard the Scottish term "wally dugs" before, and (sigh!) jumped to the conclusion that it was a reference to "woollie" because these dogs are often modelled with a thick long coat (they are usually based on the King Charles spaniel). The man who brought the dogs along thought "wally" was a reference to "wall" because they were designed to sit against a wall (hence the flat backs).

Wrong, both of them.

"Wally" (or "wallie"), pronounced "wahli", is a Scots word for china or porcelain.

It originally meant (and is still occasionally used in this way) fine, good-looking, decorative, ornamental. Through usage, it then came to mean china or porcelain, since the adjective was so often applied to fine decorative china objects. "Wally dugs" simply means decorative china dogs (though it's almost exclusively used to refer to these flat-backed mantelpiece dogs). By further extension, the plural form "wallies" (pronounced "wahliz") has come to mean false teeth, as a result of these once being made out of porcelain.

See "The Online Scots Dictionary", an excellent resource.