I have a 03 Corola LE with 54K miles. Never a problem. However, recently, my front left brake, periodically, makes a very slight, high pitched squeek---that almost sounds like a record needle going across a record. The noise is not loud, and doesn't sound like a bad rubbing, but, who knows. After some normal driving, the sound goes away...then, comes back. Of course, the noise stops when the car is stopped (so, it's not coming from under the hood). Brakes do NOT squeek when I step on the brakes.
You should have the brakes checked for wear. Given the miles on the car, the most likely source of the noise is the wear indicator on the brake pad. The wear indicator is basically a thin piece of metal touches the brake rotor if the pad wears past a certain point, like 1 mm thick. The noise is meant to get people to have their brakes checked.
If you have caught the noise early, you should be able to get away with just brake pad replacement and a caliper slide lubrication.
Jeff Strickland provided advice on how to check pad wear. The brake linings should be at least 2 mm (2/32") thick and worn evenly. If one pad is worn unevenly or more than the other pads then they should be replaced.
If you decide to tackle pad replacement yourself, I recommend using genuine Toyota pads because they are easier to fit, and get a small container of either wheel bearing grease, Permatex Anti-Seize (silver color), or brake caliper grease, whichever is least expensive.
You will need a flat bladed screwdriver, a metric socket set (I think a 14 mm socket will do the trick), and some fine sandpaper or a toothbrush-size wire brush.
The first time you replace brake pads, the job will probably take about an hour per side, once you get the hang of it, you can replace both front brake pads in under an hour. Even if you pay full retail for the genuine Toyota brake pads, you can do the job for a lot less than any discount chain.
Since you are on active duty, if you are in the Chicago area, I'd provide hands-on lessons on brake pad replacement - all you would need are the pads.
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