You will need trad gear to set up most anchors - there are some accessible routes but for your purposes you'll be best served by Declaration Crag; Plaque Wall or some of the climbs at the Organ pipes at Arapiles; or Summer Day Valley in the Gramps. That way bub will be easy to watch on a blanket while you belay each other.
Of course the best option will be to make some friends in the Pines and join them where possible! I've been to Araps several times with my little ones and we had the most fun tag-teaming parenting duties. We met with a couple and their bub and it worked very well pairing off like that.
The blue mountains is far more challenging - depending on how mobile your baby is!