My question is: Is the Datadog Exporter capable of sending data to the Datadog Agent, rather than directly to Datadog? Can you please help me?

No it's not. This might be something planned in future considering there are metrics, logs and traces that can be sent. The exporter allows you to connect directly to Datadog's intake endpoint based on the site and key parameters/fields. If you need to use the agent, then you can simply use Datadog's own distribution of the Otel collector (DDOT - which is the agent with an Otel collector processor)