I didn't have anything to drink really (apart from the occasional beer) until DD was over 1. I didn't express as I wasn't feeding her overnight

Alcohol goes out of your BM the same as it does for blood. although I did err on the side of caution and didn't feed her for 9-12 hours after, When you express while drinking you have to throw that milk out obviously. so you have to build up a supply in the fridge. My suggestion would be to look at formula tins.. Work out how much they recommend for a 4 week old and go on a little more then that. (eg they might say 5 bottles of 140ml try and get 6) kwim???

When I did drink with DD I always stopped drinking at midnight that way I was able to feed her around 9 the next morning but with a newborn that is different.

good luck and have fun (ps 1-2 drinks should be ok if you had them straight after you fed her and then you might not need to express more then say 1 bottle as a just incase)