Get a ferry to Blakeney Point from Morston to see the seals. You see loads, very close up. You have to check times as they go on the high tide [[http://www.norfolksealtrips.co.uk/ here, and there are other companies). Dress warmly and in waterproofs!
The beach at Holkham is fabulous, but could be a trek with a baby. The beach and quay at Wells, have fish and chips at French's chip shop, there is a zoo at cromer, Amazonia. Stop at the conservation and birdwatching centre inbetween Salthouse and Cley and look at all the birds on the marsh through the webcam and telescopes - see the huge rare marsh harriers.
In Cromer there is a tiny museum, and another in Sheringham. West Runton beach is nice, and you can search for the ice age mammoth fossils on display in the Cromer museum.
There is a steam engine museum at Thursford, with music played on original steam driven dance hall organs and also traction engines and a few steam fairground rides.
Cromer has a small multiples cinema, Sheringham has Splash! an 'trpoical pool' with wave machines etc, but is good for babies as it slopes in from v shallow water.
There is another steam train from just outside Wells which goes to Walsingham, a lovely litlte place with a shrine.
IMO Blickling is nicer than Holkham Hall. HH OK - don't eat in the 'Bygones cafe' - disgusting! But the cafe by the gates is OK fro afternoon tea and cakes.