How to know programmatically whether Message Queueing is enabled on the machine or not?

You can use the System.ServiceProcess for this one, but first you need to add reference to your project the Service.ServiceProcess, and you can retrieve all the services and get their status like this:

List<ServiceController> services = ServiceController.GetServices().ToList();
ServiceController msQue = services.Find(o => o.ServiceName == "MSMQ");
if (msQue != null) {
    if (msQue.Status == ServiceControllerStatus.Running) { 
        // It is running.
    }
} else { // Not installed? }

Answering little late, but if you are scripting fan Powershell is at your help. To get status update on numbers, use following script:

$queues = Get-WmiObject Win32_PerfFormattedData_msmq_MSMQQueue
$queues | ft -property Name,MessagesInQueue

This will show you name of queue and number of items in each queue. Hope this will help someone someday. :D