Well it sounds like you got 4 or 5 years out of the old battery, so most likely it will be good for quite awhile with a new battery. But you have to ask yourself how much longer you'll be satisfied with this computer and whether it is better to save the cost of a battery, sell it as-is and put the money into a new machine.
Of course 4gb is going to be somewhat limiting, but maybe not a big deal (depending of your software). I think the biggest issue is the relatively short run time of the 2012 MBA vs newer models. In 2013 they switched to more efficient chips that give run times approaching twice that of the 2012. But again, it depends on your usage pattern. 10 to 12 hours of battery time could make a huge difference for some people. May not matter much to others who usually have their computer plugged into the wall.
Another shortcoming is the slow wifi on the 2012 model. In 2013 they upgraded to 802.11ac wifi that is really fast (probably 5 to 6 times faster than yours). Again, this won't matter to people who don't have a router that supports the correct protocol. And it probably won't matter much for connecting to the internet unless you have something very fast like FIOS. But it makes a considerable difference if you connect wirelessly to shared network drives and copy big files.