You need a 'small' carrier. Look at the thread right below for product suggestions. If you want to pick up a smaller one in a store before your flight, check out your nearest Petco. They do offer carriers within that limit.
It's been reported multiple times on this board that as long as carriers are soft-sided and can be squished to fit, you'll likely get away with bringing a slightly oversized one, especially if it's just an inch in height.
I have no personal experience with Spirit. Most (frequent) travellers with pets tend to not book ultra-low-cost airlines like Spirit because of their extremely cramped seating which makes travel with a legroom-robbing pet carrier a really unpleasant experience. Unless you opt for their "big front seat" product (which has about as much space as premium seats on legacy airlines) Spirit only offers 28" of seat pitch, the lowest in the industry.