I am sort of in the same boat. My husband and I are traveling right now. I just finished up a 6 month contract, just in time for our 1st child to be born! Due March 29th! We also have two dogs and plan on continuing to travel once the baby is born. It works for us because my husband can work from home and be an "at home dad" while I can make the same amount of money as both of us working full time. We like to drive where we go. For one...dogs, two it seems like part of the adventure is being on the road. This may be a little more difficult with a hungry little one in the back seat. What the heck though, we are going to try!
With most companies I believe you can get insurance from the 1st day of your assignment. You may just check into that. That is how mine worked. As far as your housing options, I have never felt unsafe in any of our agency placements. (other than they tried to put us at an extended stay at the airport once) We quickly took stipend and found our own place.) We do tons of research to make sure we are being put into a good area. Check out travelnursehelp.com. There's some good information on there when you are planning an assignment. It has helped me make decisions about specific areas where I was offered a job. It has crime rates and you can view surrounding areas.
I wish you the best of luck. I say "Go for the Gold!" (Even with a little one!)