If there's no label designating it as a month list, I would include the name in the list item. I frequently encounter forms that don't label them and use only numbers and I never know if the first one is day or month until I click in the box. That applies more to date selectors with three dropdowns, but I like to know what an element is without thinking about it.
Also, for credit card dropdowns, the most common way people are asked about expiration dates (and the way it is represented on the card) is MM/YY in number form, so I would match that as closely as possible. The way you have it now does that because they can enter the number they're looking at on the card and it works.
As an alternative, you could do just text boxes which I prefer as a user because it's less clicking.