To retrieve data from Datadog, you'll need to access its API. Begin by logging into your Datadog account and navigating to the API section. Here, generate an API key and application key. These keys will authenticate your requests to the Datadog API.

Determine the specific data or metrics you wish to move from Datadog. Familiarize yourself with the Datadog API documentation to understand how to query the data you need. This might include metrics, logs, or events.

Develop a script using a programming language like Python. Use libraries such as `requests` to make HTTP calls to the Datadog API. Set up your script to authenticate using the API and application keys, and to fetch the desired data. Make sure to handle pagination if retrieving large datasets.

Once you have fetched the data, check if any transformation is required before sending it to RabbitMQ. This could involve formatting the data into JSON or another structure that RabbitMQ can easily process.

Install a RabbitMQ client library appropriate for your programming language (e.g., `pika` for Python). Use this library to establish a connection to your RabbitMQ server. Ensure you have the correct RabbitMQ server credentials and know the queue or exchange where you want to send the data.

With the connection to RabbitMQ established, modify your script to publish the fetched (and possibly transformed) data to the desired RabbitMQ queue or exchange. Use the RabbitMQ client's API to perform this action, ensuring data is correctly formatted and routed.

Enhance your script by adding error handling to manage potential issues such as API rate limits, network errors, or RabbitMQ connectivity problems. Implement logging to track the success of data transfers and to ease troubleshooting if issues arise. Consider using a logging library to capture detailed logs of each step in your data transfer process.

By following these steps, you can effectively transfer data from Datadog to RabbitMQ without relying on third-party connectors or integrations.