Hi there, congrats on your new baby!!!
since she was 3 weeks early, this means her acctual age is 2 wees old, i remember when my DS was that age, i didn't kept a schedule per se, i just tried to follow to the order of things of EASY, not feed to sleep and so on. So if he woke up hungry after 2 or 2.5 hrs after his last feed i would feed him then (never before the 2hr, 'cause my ped told me not to do it before 2hr and not let pass 5 hrs between feeds) and give him some activity and then sleep again. It wasn't until he was like 2 months old that i acctually started the schedule of 3hrs 'cause he was hungry pretty much every 3 hrs. So my suggestion would be not to worry about the 3 hr mark, and just try to keep to the order of EASY, when you start to see a more stablished hungry time, then start with the 3 hr mark. but that's is just MHO.
HTH