Is there a developer edition of WebSphere MQ for free download?

There is a developer edition of Websphere MQ 8 and 9 for Windows and Linux.

You can grab it here: https://developer.ibm.com/messaging/mq-downloads/

There is trial version of WebSphere MQ available for free download. The trial version has all features that you get in enterprise 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 available. It's a 60 trial. You can download it from here. If you don't want to download the trial, you have the option of sandbox and cloud which is available on IBM SmartCloud and Amazon EC2.

Update: There is also developer edition of WAS available here.

As far as I can see MQ is not included in WAS 8.5.

I know it is an older question, but here are my two cents:

A docker image for IBM MQ can be downloaded from hub.docker.com This image is free to be used with development.