There is a trial version of WebSphere MQ available for free download. The trial version has all the features that you get in the corporate version. You can use it for 90 days. Here is the download link.
There is also a trial version of WebSphere Application Server v8.5. This is 60 samples. You can download it from here . If you do not want to download the trial version, you have the sandbox and cloud option available on IBM SmartCloud and Amazon EC2.
Update: There is also a version for WAS developers here.
As far as I can see, MQ is not included in WAS 8.5.
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