At 3 months I'd be happy to take my little one in a baby bjorn for a pootle to the shops. The missus however would not be happy, so clear any purchases first! Plus if I walk then 8 bottles of ale will fit comfortably under her pram where as the bike handles poorly when they are hanging off the handlbars 😉
Another issue I have with a baby bjorn is that most contintental kids are carried on sit up and beg city bikes, while all my bikes are lower bars and stretched out, which limits the space in front of you and would effectivley have the baby looking at the floor.
Do you feel the need to wear a helmet? If you do then I'd suggest that your first born needs one too (trailers excepted), and their head control won't be good enough until 6 months ish to wear one.
If I were you I'd just wait until next spring, you'll have plenty to worry and between now and then other than bikes!