We have the same issue.
We migrated from running our own RabbitMQ instance into Amazon MQ which is an unmanaged RabbitMQ service. The guide suggested by @nmcnamara only works if you have shell access to the box and can install additional software. However, in the case of AmazonMQ, you don’t have shell access and cannot install the newrelic agent.
So the question is, does NewRelic support metrics coming from AmazonMQ (AWS RabbigMQ service)?
The documentation provides with references which don’t appear in NewRelic itself AWS integrations metrics | New Relic Documentation
Also, all the dashbords for AmazonMQ are empty except the one that shows the total connections.