I am planning to apply for an auto loan to purchase a car in the next couple months, but checking out the process for prequalification, I noticed that a common question asked is length of time at my current residence. I will be moving in two weeks and will be in a rent-free situation afterward, but I will have zero months at my new residence. Given that I have very good credit and a stable job that I will not be leaving, will this adversely affect my application?
If you have good credit and have income (stable job), I don't think it should matter. Like Keshlam said, you should at least let them know. However, fyi, the length of residency does get taken into consideration since it gives the creditor somewhat of a clue about your stability along with other information you give them.
The two answers you received are spot on. Creditors look mainly at credit worthiness and your ability to pay. Often when they run a credit report, the credit report will show the other places you lived and may give them some information about your credit worthiness living somewhere else...for instance, were you late with a utility bill?
Otherwise, it should be a smooth process.