The Australian spelling is penelopise and the American spelling is penelopize.
It relates to having a way of gaining time when you're putting off something you don't want to do. In the original case, Penelope, the wife of Ulysses, wanted to stave off agreeing to marry any of her pressing suitors, because she hoped her missing husband would come home. (He did.) She said she'd choose someone when she'd finished a tapestry she was working on. Each morning she would pull out the work she'd done the night before.
So, each time life is getting me down with too many stresses, I can penelopise, by simply walking out the door with Penny and setting off to enjoy the neighborhood. We all know that as soon as you come indoors from walking the dog, she's ready for the next one, so it's just like Penelope's tapestry.
Penny's not actually named after Penelope. She's named after the penny coin, because she was such a lovely copper color as a puppy.
If you'd like to read more about this word, I've blogged about it over on my Word Blog.
