What does lorelai mean when she says "Oi With the poodles already"

She means nothing によって it. She just noticed that "Oi" was a funny word as well as "Poodles." She thought that it would be brilliant if あなた could make up some kind of a catch phrase. And thus, "Oi with the Poodles already!"

I've always took it to mean something along the lines of "Oh, enough already." But to each his own I guess lol.

I always took at as "Oh God!" But maybe i'm wrong?