For printers without SNMP support, you'll probably have to implement a manufacturer-specific solution. If you want to write an AIR app that talks to SNMP-enabled printers, I can see the following approaches:
Implement SNMP client in ActionScript
Since SNMP is usually based on UDP, you could use flash.net.DatagramSocket to implement your own SNMP client in AIR. AFAIK, there are no ready-to-use ActionScript libraries, so you'd need expert knowledge of the SNMP protocol and a lot of development time.
Write an AIR Native Extension
With a Native Extension (ANE) you could implement the SNMP client in C/C++. This has the advantage that you could use an open source library like Net-SMTP to do the heavy lifting, but you'd still need some experience in developing and building C/C++ libraries.
Use a command-line tool
The easiest solution is probably to use one of the free SNMP command-line utilities from Net-SMTP or SnmpSoft, for example. All you have to do is to call one of these programs using flash.desktop.NativeProcess providing the correct arguments and then parse the output.