Could brake pedal squeaking indicate power brake could fail?
Probably not, but because they are brakes you should take it in for inspection. The shop might just have to spray a little lubricant in it, or they may find something that could keep you and others safe if they fix it.
Not power brake failure but maybe brake failure overall. Brake pads have little metal tabs on them that rub on the rotor and cause an annoying noise when they need replacement. Have yours checked, it may be time to replace them.