DKIM Problem with Exim/WHM

Hello, I'm very new to having my own VPS (moved over from shared hosting a week ago) and am still very much learning how to set everything up. After much tinkering, I've finally managed to set my SPF records up correctly and they pass wonderfully. Now I'm trying to get my head around DKIM, and I'm a little stuck. I have enabled DKIM in CPanel for the site/domain I want to add the records for (Cpanel states 'Enabled Active (DNS Check Passed)'). The DNS for the domain is run from my server (ns1@mydomain.com) and I manage this on my server through WHM. I can see that when I enable DKIM in Cpanel, an entry is added to the DNS file - 'default._domainkey' and then the key. However, when I send test emails I get this back: SPF check: pass DomainKeys check: neutral DKIM check: neutral Sender-ID check: pass SpamAssassin check: ham More specifically, it says 'Message not signed' in relation to the DKIM neutral. So, I've figured that EXIM is not adding the private key to my emails when I send them (yeah?!), however I have literally no idea how to enable this. I've dug around in WHM but can't find anywhere I can generate/add this. My research suggests I need to do this via the command line (which being a complete noob is something I am pretty clueless about - its next on my 'must-learn' list). So can anyone help me to fix this message not signing issue and point me in the right direction? If I do need to do this through the command line, could you possibly walk me through step by step from login? Other guides I've found on this already presume a fair knowledge of ssh/command line. Many thanks in advance!