There's no need to add a new vendor, Ma_nna.
QuickBooks Desktop allows you to select a vendor in the CUSTOMER:JOB drop-down. Let me lay down the steps that Lexiesmemere has described.
If you are using QuickBooks Online, there's another way to record an employee reimbursement. Here's a reference with the steps: How to reimburse an employee.
We are glad to get you directed to the right page when recording an employee reimbursement. Let us know if you need more help.