Create AMQP HTTPRequest calling POST /api/exchanges/{username}/{exchangeName}/publish

WebCustomSettings are custom settings in Salesforce the values are the following:
AMQP_Url__c: https://jellyfish.rmq.cloudamqp.com
AMQP_Credentials__c: xxxxxx:xxxxxxxxxxxxxxxxxxxxxxxx (username:password)

	public void callAmqpEndpoint(String exchangeName, String method, String aPayload) {
  	HttpRequest req = new HttpRequest();
    try {
      if (exchangeName != null) {
        req.setTimeout(120000);
        req.setMethod(method);
				setAmqpAuthHeader(req);
				System.debug(String.valueOf(aPayload));
        req.setEndpoint(WebCustomSettings.AMQP_Url__c + '/api/exchanges/' + WebCustomSettings.AMQP_Credentials__c.split(':')[0] + '/' + exchangeName + '/publish');
				if (aPayload!=null)
        	req.setBody(aPayload);
        System.debug('Sending api request to endpoint' + req.getEndpoint());
        Http http = new Http();
        http.send(req);
      } else {
        throw new Rest_Exception(ResponseCodes_Mgr.getCode('AMQP_REQUEST_FAILED'));
      }
    } catch (Exception ex) {
      System.debug('Error sending amqp request ' + ex);
      List<String> theArgs = new List<String>();
      theArgs.add('AMQP');
      theArgs.add(req.getEndpoint());
      throw new Rest_Exception(ResponseCodes_Mgr.getCode('AMQP_REQUEST_FAILED', ex, theArgs));
    }
  }

Setup AMQP headers

private void setAmqpAuthHeader(HttpRequest aReq) {
    Blob headerValue = Blob.valueOf(WebCustomSettings.AMQP_Credentials__c);
    String authorizationHeader = 'Basic ' + EncodingUtil.base64Encode(headerValue);
    aReq.setHeader('Authorization', authorizationHeader);
		aReq.setHeader('Content-Type', 'application/json');
		aReq.setHeader('X-AMQP-Tracer', requestJson!=null && requestJson.getTraceId()!=null ? requestJson.getTraceId() : '');
  }

Serialize AMQP Request JSON

	private String serializeAmqpRequests(String payload) {
		JSONGenerator generator = JSON.createGenerator(false);
		generator.writeStartObject();
		generator.writeStringField('routing_key','amqp-events');
		generator.writeFieldName('properties');
		generator.writeStartObject();
		generator.writeEndObject();
		generator.writeStringField('payload', payload);
		generator.writeStringField('payload_encoding', 'string');
		generator.writeEndObject();
		return generator.getAsString();
	}

Callout RabbitMQ

public void sendAmqpRequest(String payload){
		 String amqpPayload = serializeAmqpRequests(payload);
		 callAmqpEndpoint('event-exchange', 'POST', amqpPayload);
	}