It depends on the way of life you used to have. Accommodation (one bedroom apartment) will cost you ~1000 euro per month or more. Food for a family ~600 euro (excluding food and drinks when you go out).
But with 2800 after tax, you could have a normal life in Cork. One of my friends came to Cork with wife and 2 years old child and he has 2500 euro after tax, where half of the salary they spend on rent. They don't travel so often, but you always can go and explore Ireland.
After your family will be registered in Ireland, you will get some extra money for your child. Your tax will be ~20% as soon as your wife is at home and not working.