[Rudder]

So it is kind of a whine with a smile on their face

Yeah, but the "whine" is staccatic.

[Ditter]

OK we are back to square one, I have never heard a dog make a sound like that, a loud slow pant/whine that is staccato.

A cat yes, when they are looking out the window at a bird or squirrel and dreaming about catching them if they could just open that window.