When headsets squeak it might be more serious than just dry bearings which can be pretty quiet. The cause is often the skirts of headset cups rubbing on the corresponding cone, which indicated a bent steerer. Swing the bars back and forth and watch the gaps in the upper and lower headset units and see if there's any wobble. If so your steerer is bent.

BTW- All this assumes the headset is tight, because a loose headset also can squeak but that's simple enough to fix.