So this is the address my coins were sent to.
http://dogechain.info/address/DMzmYZQ8WQ7hEweEigogUbRKMgQ6yeWWU3And here is a ss of my recent transactions.

You can see the transfers into it and nothing was transferred out. Is there anything that can be done such as when sent to an exchange they could do something? I know I'm grasping at straws here but I don't want to give up so easily.
As much as I would like to help.. Thinking how would I feel to be in the same situation, I think that there's nothing much you can do. You should have kept your coins more safely and make your PC clean from all of the malware... Who knows what could've might got into it and take/compromise your data...
Just for the LOL's it would be great if there was DogePolice or something ..

... But this is not the time to be funny... I am sincerely sorry for your loss.