A limited user account won't stop a trojan installing itself, but it will limit the things that it can do and that will limit the potential damage.
To create registry entries (needed for run commands so the malware starts on boot, disabling task manager, configsys, regedit, etc.) you need admin privileges. To place malware in the system folders requires admin privileges.
So having limited user accounts will save a great deal of damage, but it won't stop everything.
Find out what the mIRC is, ensure that it is the latest version and if it has the ability to have downloads scanned do so. The file name you posted seems incomplete, e.g. there is no file type, .exe, etc. Check the avast! Log Viewer (right click the avast 'a' icon), Warning section, this contains information on all avast detections.
The reason I mention this is the Standard Shield should under normal circumstances scan newly created files (depending on file type) this is normally the executable or potentially dangerous file types. So for it to be found on an on-demand scan seems strange. It could well be that this detection signature has been recently added and the file is old.