No. You can start the call but you will receive a Call Failed notification. Just like a telephone call you - can't call yourself.
Secondly, Apple suggests that each person have their own Apple ID. You might look at setting up your child with their own one.
See Apple ID Frequently Asked Questions
Can I share an Apple ID with someone else?
Your Apple ID should not be shared with anyone. It provides access to personal information including contacts, photos, device backups and more. Sharing your Apple ID with someone else means you are giving them access to all your personal content and may lead to confusion over who actually owns the account. To share purchases, photos, a calendar and more with someone else, try Family Sharing Opens in a new window., Shared Albums Opens in a new window. or other easy-to-use sharing features.
Create an Apple ID for your child