Can it wait a little while until the baby is a bit older? Not so much for health reasons but blimey, there's no way on earth I would want building work going on with a newborn and another child to look after, not unless the house was about to fall down! Sorry, prob not that helpful but....also, will you want the noise if you're trying to catch up on precious sleep???!
It is not a good idea to expose a new set of lungs to building dust. The eight weeks of work may well run on a bit longer. Then there is the noise, disruption, and trying to care for a new-born & DC1 in that situation would be hazardous and a nightmare. Can you not move out during the work? Relatives? Friends? Rent?