Having studied the origins of 'Irish' jokes (there's a bit about it in my Honours thesis on racism, as well as many respected publications on Irish racism!), I can't just let it 'roll off' - they are as insidious as Jewish jokes, in all honesty. This term 'Irish Twins' is another example of those origins - I mean, there are other Catholics in the world, aren't there? And even non-Catholics who don't use contraception and have kids very close together? This is me raising an objection to the term - common usage doesn't make it right, to me. Bring on the 'rolleyes'!!
Anyway, just to say it's different for everybody. I have neither fallen pg nor had a period since DS was born and I obviously don't rely on the mini pill (or I wouldn't miss it from time to time!) I'm not saying this as 'proof' that you won't fall pg, just as an example of how there is no flat rule about it either way. Some people just don't ovulate for at least 2 years after birth, some do right away. So, you gotta weigh up the risks and decide how vigilant you'll be and what measures you'll implement