Based on the information you provided, I would definitely not recommend purchasing the car right now. Mainly because:
I'm living at home for the next 2 years.
Your main concern may not be as bad as you think:
I don’t want to have to be stuck on the side of the road scrambling to buy a new car because my 13 year old car broke down while I’m in college.
Although breakdowns happen, it's far more likely that you'll see a fluid leak, start feeling something is off, or hear some strange sounds before it breaks down, and then you'll take it into a shop and learn the bad news. But even in your breakdown scenario, you're only an Uber/taxi or phone call to family/friend away from a ride home or to school. Your 13 year old car might continue to last you for the next 2 years or even longer.
The first thing I would do is have your existing car looked over by a mechanic that you trust. You basically want to know if it is safe to drive as is, and what kind of future repairs they would anticipate in the next couple of years.
Then, I would continue to save like you're doing. If your current expenses are low it's possible that you could save up to $10K per year, and if you achieve that you would be in a far better position to purchase a nice car, perhaps even the one you have in mind without even needing a loan! (That being said, even if you had the full $23K saved up right now, I still wouldn't recommend spending your entire savings on a new car.)
Some other things to consider that make purchasing now risky:
- What if you lose your job?
- What if school + working as much as you do now including your side jobs proves to be too much? Depending on your course load and your current work hours, you may decide to make changes.
- What if your home situation changes such that you need to start paying rent or find your own place?
All that being said, you did mention you want a "super safe" car. Surely a newer ear will have better safety features than your current car and this could tip the scales towards a different car, though not necessarily all the way to a brand new car. For example, rearview cameras and sensor alerts may be especially useful for newer drivers. The importance of these types of features should weigh into your decision, though it's difficult to assign a monetary value to them.
Lastly, also keep in mind that newer drivers are the most likely to get into a car accident. Collision insurance might be a good investment regardless of what type of car you have.