Hi Mark -
Working part-time should not be an issue as long as the two of you have an adequate income and both have been employed long enough to show stable employment. Lenders generally want to see at least two years working in the same job or field, so you would meet that standard, as would your girlfriend as well if she has had steady employment for the last two years.
Another issue is your credit score. Since you have a credit card, I assume you have decent credit. However, if you and your girlfriend are going to be joint applicants counting your combined income, lenders will look at the lowest credit score of the two of you. If she does not have good credit, you might see if you can qualify on your income alone. You can qualify for an FHA loan with as little as 3.5 percent down with a credit score as low as 580, though not all lenders will go quite that low.
A third factor is how much debt you're carrying on your credit card. As a rule, no more than 41 percent of your gross monthly income should go toward debt payments of all kinds, including the new monthly mortgage payment (including property taxes and homeowner's insurance) in order to be approved. So if your monthly minimum credit card payment would put you over that, you should try to pay down your balance first.
Hope that helps. Good luck!