I'm guessing you mean you don't have a balance on your credit card, right? That's the amount you put on it and pay off every month, zero balance? If so, that's great. Stay that way. Credit Card debt is an emergency and should be taken care of first.
You are doing a great job with your budgeting, in my opinion.
You take home $2600/mo and spend about $1800. That's not a lot left over, as an absolute number, but it's a very well budgeted situation with a good portion left over at your income level. Congrats.
Your current car payment + insurance + gas + maintenance/tires,etc - I show that equaling about $100,000 over 10 years - conservatively invested in VTI or VOO. It's literally the maximum amount allowed to allocate to an IRA ($6,000/yr). I have no idea where you live or if having a car is required. If it is, that's ok. The numbers are pretty wild though, right?
You are in a situation where I'd say you aren't doing anything wrong, but you could do better. The question is obviously about the car. One issue I see is that you owe on the car not far off from what it's worth. You MIGHT be able to clear $1,000 - $2,000. As other said, buying a $2,000 car is risky, too. And you only owe a little more than what you should probably spend on a car $3800 (I like Sams/Financial Samurai rule). To me, all signs point to keeping the car. It's an inexpensive and perfectly nice car. Plan on keeping it for as long as you can - so that way sooner than later, that $6,000/year starts going towards YOU and not your gas powered wheelchair!
You seem to be on the right track. The key is to increase your income without inflating your lifestyle. That's the position you appear to be in at the moment and it's a good spot to be. So as you start earning more, all that should be going towards investments. Every penny. Once the car is paid off, you'll hopefully be earning more, too. So you'll start to hit a curve and accelerate your savings pretty quick.