The very first thing you need to find out, is whether a quill stem will even fit into that hole. If your steerer is made of steel then a 25.4mm quill stem will probably fit there. Keep in mind that these 25.4mm quill stems are far less common than the usual 22.2mm quill stems. They were made for MTB's in the mid/late 90's just before threadless took over. If your steerer is made of alloy or carbon, then the inside diameter could be too small to fit the 25.4mm quill stem.
As an aside, My 2 boys are around 5'1" to 5'3". I find that 650c wheel bikes work best for them. Trek and Cannondale both made 650c wheel road bikes from the mid 90's to the mid 2000's.