As Scott mentioned it depends on what type of loan you getting. Guidelines are almost the same for lenders expect the underwriter conditions that's every lender has is different all based on credit and risk factor. To answer your question, you will have to clarify something to your lender, did you have a part time job before prior to your current part time, if yes.. Was it in the same line of business? If yes ,, yes we as a lender will count that income.
Before going out house hunting, you should go to a lender and get qualified , when I say you get qualified, means take your income documents., assets statements and work with your lender on the approval. I have some lots of mortgage origination issuing approval letter based on verbal information they got from borrowers however when the loan is ready to process they can't qualify them anymore because there was something the borrower did say!
Also its recommended because sometime you may find inaccurate information on credit report that you may better off delet of your credit before applying for a mortgage. Always ask for a copy of your report to insure accuracy and to prevent any surprises.
Good luck with your house hunting.