Problem is, there are lots of things that can cause that type of noise. Some bad, some not so bad. One thing that is fast and easy to check for someone with a wrench, is the idler pulley on the fan belt.
Its spring loaded, so you just put a wrench on it, lever it away from the belt, and spin it by hand. If the bearing is going bad, it will either feel loose, make a noise when spun, or both.
As for the dowel test, all you need is a worn out broom or mop with a wooden handle. Cut the head off, place one end on, say, the alternator housing, and press the other end against your ear.
You will usually hear noise, but the bad unit will be making the same noise you hear now. It will just be a lot louder.
They sell mechanic's stethoscopes that look like a doctor's stethoscope but with a long probe on the end, but if you can hear the noise plainly from outside, then usually the dowel is all you need.
Oh, and just for the fun of it, check the transmission fluid. If it were low, it might make that noise, but I would expect you to see shifting problems by now. But its always a good idea to check the transmission fluid.