Don't worry about dirt on your dogs feet as very soon your baby will be stealthily chewing on some quite disqusting things anyway- even if you watch her like a hawk, they always manage to get a hanful of mud, dead insects, oh, I could go on...
Who's poo traces? Again, if the dog is vaccinated and dewormed, your baby will NOT get anything serious from that. Promise.
It's normal to be anxious a bit- I remember being a bit paranoid about other people touching DD's hands in shops etc for fear of passing any germs to her, but then as they grow you have to let go to certain extent. For example, now that we go the children park every day,what am I supposed to do? Wipe her hands every time she touches the equipment, so she doesn't pick up any bugs off other kids? Rinse her mouth every time she manages to shove some sand in? Nah, it would drive me (and her) mad.
If the dog is gentle, then, really, don't worry. I guess there's always a chance he could bump her or scratch her when dancing with excitement, but that is very unlikely to cause any serious injury and just keep an eye on him til your baby is a bit more robust.
Plenty of kids are raised with animals and do just fine.
It seems you love your dog, so it would make you very sad and feeling guilty and, obviously, it would be very traumatic for him.