I would probably replace the car when possible. I would look into what the cost of repairing the A/C is, since that will greatly cut down on the value of the car if it isn't fixed. Might be best to fix the A/C first anyway, but I agree heading toward a new-to-you car is probably the right direction.
Having said that, you are not in an emergency with the car, going without A/C isn't that bad, and you need to slowly and carefully consider your car situation and head toward where you want to be. You don't mention your financial situation, and that is what should dictate your decision right now. I currently am driving a 2005 vehicle with 160k miles and rust eating at the body. Oh, and the A/C is broken just like yours, there is dye coming from under the compressor so that will probably need to be replaced to make it work. I have enough money in the bank to pay cash for a nice used vehicle, but I don't. I could certainly repair the A/C, but it's just not a priority. My kids hate the lack of A/C, and I tell them to suck it up. It's a good experience for them. Your new baby wouldn't be able to "suck it up", but it wouldn't be damaging unless driving a long distance with the windows up.
What is my point? The point is growing your badassity muscle is worth it! Who the hell cares what your vehicle looks like! Who the hell cares if you sweat a bit and get sticky! You replaced a door on your car, that is sweet. You handled lack of A/C for a summer, that is awesome. You are showing yourself that comfort isn't the priority, and being badass isn't a bug, it's a feature. So when you have the money pulled together, and when you know the right way to go (read the car post by MMM), then make that move in a deliberate way and be happy with the new vehicle with A/C. Nothing wrong with that. But don't "suffer" through your current badassity, revel in it!