Don't get rid of the cat; make him scrub out your brew kettle as punishment.
I'm having a hard time visualizing what happened. You had about 1/3 of the starter leak out through the airlock after your flask tipped on its side? Was there a way for dust-borne nasties to get inside? If you think the starter stayed effectively sealed from the open air, you're probably fine. After 9 hours, you've likely got enough of a population to effectively compete with most other things. I'd add a bit more boiled and cooled wort to the starter to see how it responds, and to see if you get any funky off flavors.
If it really was wide open, though, I'd consider getting some more yeast. It's probably fine, but I'd hate to waste a brew day and however many weeks of waiting just to save $7.