Cruiseline Deadline for Pass Port

Hey everyone. I am looking into research on taking my first cruise. My husband and I are excited to finally be doing this.
Here's the problem. Since we have never been on a cruise before, we are not familiar with the policies as far as passports. Hubby has travelled abroad before and has a passport. Neither me nor the baby have gotten a passport yet.
We're looking at booking in August since that is the only time we can take off from work.
Can anyone tell me the Crusie line travel deadline for a passport? How long does it take to have a passport issued and when does the cruise line need to see it? Can I go to any country in the cruise with the passport? I'm sorry to be a bother, but I am new with this.