Do a Google search for "domain name generator" which will bring up a pageful of results. Use any of them and type in "baby" and click enter. Any generator will give you a ton of options and ideas. Keep to a dot com domain as they are considered the best. Lastly, purchase the domain here so that you can have all the parts of your online business in one place.

Hope this helps.

Try jaaxy

Research in menu on the left

firstbabychecklist or firstbabyessentials
i prefer the first one as you can cover what to do with the body, the house, the car , visiting, holidays, etc
it is a broad niche so make sure you pick one section and try to cover all the needs in that first.
ask your audience what they want you to cover - go onto forums and ask in there what they would like to have seen or would like to see/know
make it interesting and memorable
good luck
( and good luck with your daughter's pregnancy)
phil