Log DNS queries with iRule?

Which version of code are you running, and how is it licensed? If the dns profile is applied to the Virtual Server, you may have access to a set of these primitives:

• https://devcentral.f5.com/wiki/iRules.DNS.ashx

Alternatively -- and more easily -- if you have a version that supports it, you can use a DNS logging profile:

• Manual: External Monitoring of BIG-IP Systems: Implementations