Is it possible to use iRules to replicate a very basic DNS

I did address the question before I provided alternatives. 🙂

You missed this line:

Check out this page, it has examples: https://devcentral.f5.com/wiki/iRules.DNS__answer.ashx

Check out the link, there are examples. On an LTM you will need a DNS services license. On a GTM you are good to go.

Here is one of the examples:

 Send one or more IP addresses for a response to an A query
 Use on an LTM virtual server with a DNS profile enabled
when DNS_REQUEST {
     Log query details
    log local0. "\[DNS::question name\]: [DNS::question name],\
        \[DNS::question class\]: [DNS::question class], 
        \[DNS::question type\]: [DNS::question type]"

     Generate an answer with two A records
    DNS::answer insert "[DNS::question name]. 111 [DNS::question class] [DNS::question type] 1.1.1.1"
    DNS::answer insert "[DNS::question name]. 111 [DNS::question class] [DNS::question type] 1.1.1.2"

     Stop further processing of the query after this iRule and send the answer to the client
    DNS::return
}

HTH