Do i need AWS RDS if I use postgres and docker-compose? My dock

It depends on what kind of application it is, but it is safer to manage the database in a managed environment such as RDS than in a container.
In addition, the use of managed services is likely to make management easier, as basic security and other services can be left to AWS.
Database backups can also be performed using RDS automatic backups or AWS Backup.

If you don't want to create RDS database, you can mount a EFS to the host/docker and set the postgres database volume to the efs mount. I have used this for a Jenkins server running on Fargate, check this https://aws.amazon.com/blogs/compute/using-amazon-efs-to-persist-data-from-amazon-ecs-containers/