8 week old not smiling

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I took my 8 week old to their check up this week and doctor flagged that she isn’t smiling yet or following with her eyes. He has asked us to come back in 4 weeks and has said he will refer us to a paediatrician if she still isn’t doing it by then. I’ve now got myself into a total state over what this could mean. I’ve had the odd smile here and there but definitely not consistent and you have to really work for them. Yesterday I managed to get her to follow an object with her eyes but today she doesn’t seem interested.
I have 3 under 3 and feel like this is my fault for not doing enough with her- I try to give her as much attention as I can but it’s pretty crazy!
Has anyone else had a late smiler/ eye following baby and all has gone on to be ok?
thank you x

I've just checked my photo frame with her milestone cards. She was 11 weeks corrected when she smiled and all is fine here. The doctor has given four weeks because the odds are within those four weeks she'll come on nicely. Try not to worry. All your children will develop differently.

DD2 is 8 weeks old and we are lucky if we get a smile a day at the moment! She's quite a grumpy baby generally though Looking back at photos, DD1 didn't really start smiling enough to predictably catch it with a photo for another couple of weeks.