Level shifter circuit for bipolar battery
What you want is a voltage reference, not a level shifter.
There are many ways of making a voltage reference, but the easiest and usually the most stable and precise is using a dedicated voltage reference IC.
1.6V is a rare value though; I would use an adjustable one, like the LMx85-ADJ, but that is mainly because I have some of those lying around; there are many others. A Google search will turn up a great many (and many more for 1.5V than for 1.6V).
You will have to do some math to calculate the resistors needed to run it off 9V and to set the voltage you want, but the datasheets will show you how it's done.