We're lucky we have no major dog allergies or excessive moulting problems in my family, and the children have been shown dogs from being a few months old, usually with the dog on the lead and the children sitting with a vantage point where they won't be licked. My 19 month old twin grandaughters have met my dog a few times, but haven't touched her yet (they do have a cat who decides how much contact he will allow them). Their 4 year old cousins spend a lot of time with my dog - they adore each other, and it's wonderful to see them playing together. The dog even queues up to go on their little slide with them, and will willingly take instructions from them.
The relationship between dogs and children can be something very special. I grew up loving dogs, and they have enhanced my life. I always hoover thoroughly before the children visit, the dog isn't allowed on furniture and is definitely not fed from the table. She's well-trained and has learned that children can be rough and tumble but she can't. I would never leave a child unsupervised with a dog, no matter how much confidence I have in them.
I hope some flexibility is eventually allowed, Failte81. When children get to two or three, they can start enjoying playtime with lovely family dogs like labradors. Perhaps taking the dog along to fun open air treats like a picnic with a game of rounders or frisbee woud suit your DIL better when the baby is bigger.