Actually, when I think about it, even if your banjo is not so good, you should be able to get decent harmonics on the 12th fret.
You have to make sure your intonation is correct. Use a tuner and tune a string. Then play the string at the 12th fret. It should be in tune, the same note one octave higher. If it is flat, then move the bridge forward, towards the peghead end of the neck (remember the mnemonic: flat forward). If you are sharp, move the bridge back towards the tailpiece. Each time you move the bridge, you have to re-tune and then check the intonation.
Follow Ben’s instructions about getting the harmonics and they should ring out (maybe not as nice as Ben’s great sounding Gibson banjo but you should be in the general ballpark).