Andy, I'll second the vote for testing the battery if you want to be sure. Don't replace it based on age. Unless you also notice slow starting, chances are it's OK.
At normal driving speeds your alternator puts out enough current to re-charge the battery and run all of the usual accessories, including A/C. If it doesn't, the alternator and/or voltage regulator need to be checked.
You can monitor charging system performance if you have a volt display in the dash. If there is more current draw at idle than the alternator can provide, the battery makes up the difference by discharging. The voltage may drop a bit. When you accelerate to and drive at moderate RPM, and your charging system is up to the task, the alternator takes over the load and recharges the battery. The voltage goes back up.
Now, if you had an in-dash ammeter, you'd see it move over to indicate Discharge at idle. On acceleration it would swing to Charge, the slowly drop to "neutral" when the battery was recharged. I guess all of this gauge movement was way too complicated
for most driver/operators to understand. Some even thought the system wasn't working unless the needle was 'way over in Charge!
So auto manufacturers dropped ammeters some years back.
Oh for the good old days! The last in-dash ammeter I had was in my '72 Duster 340...
By the way, running the A/C puts more mechanical load on the engine (driving the compressor via the belt) than operating the blower motor puts on the electrical system, so don't turn off the A/C just to save the battery. The headlights draw a lot more, and you don't want to turn them off when they're needed!