The oil does get old after 3 months, so the best thing is to change it then even if you haven't racked up the mileage. BUT that's the optimal thing to do. There's still plenty of room between optimal and risking your engine. I'd say you could go six months every now and then without a problem.
If you're going to go longer than three months, do it in the summer. Cold winters are more stressful on the engine, so that's when you should invest in more frequent oil changes.
By the way, I've read many times that you don't need to change the oil every 3000 miles, that most cars nowadays only need it changed once every 5000 miles. (Nowadays means anything made from the late 1990s onward.)