I just create a new EC2 instance on Amazon, with default options, and there is no way to associate an Elastic IP with this instance. The options are not available, and I haven’t reach my limit.

AWS added automatically an public ip, but I am afraid that this is not flexible as an Elastic IP (I will install Nginx on this instance).

Anyone knows what networking configuration I need to change to AWS allow me set up Elastic IPs?

From the availability zone it seems your Instance is in a VPC so when you are allocating a new Elastic IP be sure you are allocating the IP address for a VPC as classic Elastic IP cannot be attached to a EC2 instance in a VPC. Once you allocate Elastic IP you will be able to associate that elastic IP using your method.

Check this screenshot.