For what it's worth, when my son was born (1985), my wife was in the hospital about 60 hours (she went into labor in the night), so 2 and 1/2 (days) after the baby was born she and baby was released from the hospital. Two days after that, we were all out Christmas Shopping a the mall. I carried the baby in an open gym bag slung over my shoulder. His little feet were sticking out of the bag. Everyone passing though it was a baby doll until they looked inside.
It wasn't camping, but if we had a camper at that time, we probably would have gone. It was about 6 months later we went camping to Ocracoke Island (Outer Banks of North Carolina when I was in the Army Stationed at Fort, Belvoir, VA - near Washington D.C) (in the back of our pick-up truck).
It's hard to believe this little baby is now 31 years old and has a 4 1/2 year old little boy himself. These were taken (1986) when we went on a camping trip (tent and the back of the pick-up truck), when he was about 6 months old.
Yup! That's me in 1985 when in the Army. I still had hair then and could still get into a size 32 pair of jeans! (no longer)
There is nothing wrong with take your new baby camping, even days after birth, as long as everyone is healthy and up to it.
We've been taking our 4 year old grandson camping with us, almost since he was born too, when Dad let us.