I don't have a routine really, it's just led by her - feeding on demand. If I want to take her out in the pram I make sure she's fed and has been awake a while so she'll fall asleep. too knackered to impose any roles/routine yet!
At 2months both of mine were doing as yours is. I don't think you can have much of a routine at that age... Just keep daytime feeds bright and lively and night time quiet and dark to help distinguish day and night - it helped mine.... they began sleeping for longer around 8 weeks ish but all babies are different !
Just wondering what your routine for your 2 month old is? DD seems to sleep or feed most of the day. I try to play and sing to her for an hour or two per day. We go out on errands most days and also go to mother baby yoga. Just wanted to see what others are doing and whether we are doing ok?