Should I buy a life insurance policy for my baby? What companies have policies for babies?

If it's like owning a 529 plan, then why not just own a 529 plan and avoid the expense of a whole life insurance policy? If you need life insurance, buy life insurance. If you need college savings, open a college savings plan.

There are several insurance companies that offer life insurance for babies.
 
Among the leading carriers are Globe and Gerber Life. Globe offers the Globe Young Adult Plan, but they offer it to infants, too. And Gerber has the Gerber Grow-Up Plan for kids.
 
Globe Life is rated "A+" Superior by AM Best Company and offers up to $30,000 of coverage with a policy that builds cash value. The Gerber Plan offers up to $35,000 of coverage and that builds cash value as well. I think Globe Life may have a higher financial strength rating than Gerber.
 
Make sure you understand how the premiums and coverage work, and what options are available to add more coverage in the future, when your child reaches age 18, or 21.
 
Starting a plan now may guarantee your child future insurability allowing for more life insurance to protect their own family some day. And, your child has cash value building which may allow for a loan to be taken from their policy some day, if needed.
 
You can learn more by reading this article on Globe Life vs Gerber Life.