You may want to buy life insurance on your children to help pay for Burial expenses, but the best way is likely just a child rider on your own life insurance policy. That would give your child a small amount of life insurance ($5,000 to $7,500) added to your life insurance policy for a small additional premium.
As far as locking in rates goes, generally no life insurance company will issue preferred rates to a child, so that's not necessarily a good argument unless the child develops a health condition. This is another reason to buy child life insurance coverage, to protect your child in case he/she develops a health problem later in life. They can continue their life insurance coverage into adulthood, and may even have an option of increasing the amount of life insurance coverage.
Here's how you can learn more about life insurance for children.