This seems normal to me. I'm guessing the AV is reporting a false positive for mIRC. This is something you should take up with your AV vendor's support techs/forums- they would have a better explanation as to why this is the case and hopefully a way to fix it. As long as you have that AV software running, there's little we can suggest. To answer your questions in full, however:
Is this normal?
No, AV software should generally not call a chat client a keylogger. This either means the client is compromised OR it's a false positive. In my opinion I can conclude with fair certainty that the case is the latter.
Should I be worried?
If it's a false positive you should not really be worried. If I were you, I'd be more worried about the loss of functionality due to my AV diagnosing my system incorrectly.
Is this a normal function of mIRC?
It is not a functiona of mIRC at all, normal or otherwise. mIRC is not a keylogger. If the client was compromised, however, it could be made into one-- but again, this goes back to question 1.
