Hi Rollercoaster!
You'll be grand! My DS is now 9 months and we've flown over to Ireland to visit my parents quite frequently (just the two of us). First trip when he was 8 weeks old.
Not sure about easyjet & passport, but I've only ever needed his birth cert with Ryanair, Aer Lingus and Aer Arann. It was checked at Dublin Airport Passport control, but we've never been checked at either Shannon or Cork.
I always found it easier to have DS in travel system right to door of the plane. Mine is one where the car seat clips into the pushchair, so when we get to the steps of the plane, I take car seat off (with DS still in it), leave that on tarmac while I fold the wheels, then take DS out of car seat and on we go! (first time we travelled, I had him in sling which was really handy but with a bad back I couldn't carry him for long so it was great having travel system)
Staff are always really helpful especially if you're travelling alone with baby. Don't be shy about asking cabin crew to hold baby while you fold/unfold buggy, and even getting yourself settled in your seat.
They're usually delighted to get a cuddle of a baby! and don't forget, there's usually lifts at the departure gates for disabled passengers. They'll leave it at the bottom of the steps again when you land, which is great for getting to baggage reclaim (and it means you're not trying to pull case, car seat and buggy off the belt while holding baby, and if you're flying into Dublin, there can be a huge queue at passport control so you may have to wait for a while - again not an issue if you're ok holding baby and changing bag etc for that long)
My travel system also is one with two handles rather than one straight bar, this is also great if you've got a case on wheels with a pull-up handle. Just hook it over one of the pushchair handles and off you go...no need for an airport trolley!
Sorry that was a bit long-winded! But hope it helps! If you need any advice re Ireland etc, just ask!