No, but you can imagine what it is. It's an association for owners and breeders of curly-haired little dogs. They get together and discuss their dogs, and probably organise competitions and awards for the finest looking specimens.
This is used as an example of a totally innocent and non-political organisation. Apologies to poodle-lovers, but poodles are considered rather a silly looking little animals - especially when owners cut their coats in fluffy pom-pom styles and put little ribbons on their heads. It's mentioned to demonstrate how ridiculous the HUAC's ruling is. A trivial-sounding association like this could potentially be seen as being a dangerous Communist organisation, simply because it hasn't condemned the Soviet Union.