Create a User data script, which would fetch the public IP of the instance and send it via curl to you destination.
To get the IP you could either hit the instance meta data service-
curl http://169.254.169.254/latest/meta-data/public-ipv4
or some other general public IP finder-
curl ipinfo.io
Sending to a destination would simply mean crafting a curl payload and sending
curl -XPOST http://<destination>/ -d {ip: <IP here>}
Over all the script should look somewhat like-
ip=$(curl http://169.254.169.254/latest/meta-data/public-ipv4)
curl -XPOST http://<destination>/ -d {'ip' : $ip}
Just Put this script into the user data for the Launch config for your ASG.