An emergency fund of $5000 seems on the low side and I would be worried about spending it down to $2000, that said you want to get out of the car loan. It sounds like you have a little extra disposible income since you think you can rebuild your emergency fund quicker than just the amount you will save from not having a car payment. One option to decrease the hit to your emergency fund is to save aggressively for a month or two to increase your emergency fund by a few hundred dollars and take on some other debt (possibly credit card). You could then pay off the new debt and replenish your emergency fund over a slightly longer period.
While some financial planners dislike the idea of an emergency fund while still having high interest debt, to me I would prefer to have $1000 in credit card debt and $3000 in an emergency fund over $0 in credit card debt and $2000 in an emergency fund. Given your time course of 6 months or so to pay off the debt, you might even qualify for a 0% credit card introductory rate (or balance transfer).