First of all, congratulations on your new addition, wishing health, happiness and long life for all.
Some great responses, here, TVRodriguez is right on the money about guardians and trustees.
As someone who was widowed at 31, with very young children, I wish this was a conversation my late husband and I had had. We thought we were fairly responsible about money. At the time of his death (at 37, in a car crash), we had no debt, some savings and assets, but not really enough life insurance for a surviving SAHM with three children to see through college. We had the equivalent of a year's salary through his work; and a $50K private policy. That number really should have been $500K. I did ultimately collect on the uninsured motorist clause of our auto insurance policy, but it took awhile. The above estimates on social security survivors' benefits are fairly accurate, but max out for a larger family. The "pot" is shared.
While I've managed pretty decently, a larger cash cushion would have been a huge relief during what was simply a horrible time. I had to make decisions more hastily on where to live, going back to work, and even preschool and health care expenses that were different from the original plan we had for our family.
I now have a $500K term life policy on ME, with an up-to-date will and trust for my still-minor children.