Yes you can but it's a very long journey (an incredible 7 hours I think).

Dublin has two ports which both have ferries going to Anglesea. P&O go from one and Irish Ferries go from the other. There is hardly any journey difference between the two.

If you are getting train to Dublin then you would be better going from Dublin Port rather than Dun Laoghaire.

It may be worth checking out http://www.ryanair.ie because you may just get a very silly priced flight from Dublin to Liverpool. They currently have some £9.99 offers on (but don't know if they apply to that journey)