Recreational & Family - Babies, dogs and holidays

I have a baby born in January this year and have been wondering if there's any way to go biking with my whole family this summer. How old can babies normally start using bike seats or trailers? Which is safer? I'm definitely not going to want to start too soon.

Another thing, has anyone experience of travelling with their bikes and biking with young children? I live in Iceland and we have a lot of calm country roads and would love to include biking in our holiday plans but of course prefer not to leave our young baby at home. Maybe this won't be possible this year but there's always next year.
Isn't a bike seat a better option for space reasons? Or are there travel-friendly trailers out there?

Also, since I'm writing this thread I'll add this question too. Dogs. I have a very energetic little Border Terrier and would love if anyone has some insight into biking with their dog(s). Has anyone taken them on longer trips? How do you do it and what is there to watch out for? I'm definitely worried about the dog getting sore paws.

I'm not sure how old a baby should be before going on bike rides. It seems you might find a bike seat that is as secure as a car seat, but I think your baby should be at least able to hold his head up first. My kids are adults so I've not researched that topic. I do know there are a multitude of bicycling trailers for dogs, as well as dog-specific baskets for your handlebars, or baskets that sit on a bike's rear rack. Our small dog goes with us on bike rides and he enjoys his trailer very much.