You can call the IronMQ thru the HTTPS API.
See IronMQ REST/HTTPS API for more information.
Of course, you will need to provide Project ID and Token to JavaScript code. I suggest to encrypt Token before you place it into JS/HTML and decrypt on page load or before using the API.
Welcome Iron.io Live Chat even you will need more information.
Upd: For now it seems does not work. Because of Cross-Origin restrictions. But we're working on it, so, stay in touch.