There is a plugin at Nagios Exchange to monitor Exim's Mail Queue:
check_eximailqueue.
Put this script into your Nagios plugin directory. Adjust the paths to utils.sh and the exim binary if necessary.
On Debian you need to install nagios-plugins-basic first and use the following
paths:
. /usr/lib/nagios/plugins/utils.sh
EXIM=/usr/sbin/exim4
Install sudo if necessary.