It seems like at that scale length, with normal strings, you might want to tune up a minor third. My reasoning is, your scale length is about 4/5 standard, and if you apply that ratio to the 12 semitones of our scale, you chop off three of them.
Another way to look at it is to measure out 20" from the bridge on a standard guitar and see what fret it lands nearest to. Then tune the small guitar like you would a normal guitar capoed at that fret.
Or, if you want it at standard tuning, you'll probably need much heavier strings (and your low E might not sound too good).
Hi Geo, you are right. I was reading this (smallguitars.com):
to get a stable sound and tuning in mini electric guitars we recommend either using higher gauge strings (0.11 would be a good choice), or alternatively, use a higher string tuning, such as A-D-G-C-E-A or an open G: G-D-G-B-D-G. Please refer also to the section below about how to tune a small guitar)
Maybe I try a thicker string set (0.56 - 0.11) or tune it up, not down