Why couldn't the following circuit have an active transistor?
It will not work. The emitter follower has no voltage gain and an offset of about 0.7V so it will reduce your 1.8V to about 1.1V. 

The problem is that the emitter voltage increases when the transistor starts to turn on, meaning that your Vbe changes. 

You can use it in common-emitter fashion (ground the emitter and take the signal at the collector with 1K pullup to +5), however the signal will be inverted. You can add another transistor and resistor to invert the signal again giving you a level-shifted signal of 0/5V. 



Edit Eg.







simulate this circuit &ndash; Schematic created using CircuitLab