G'Day, and welcome to the forum!
When you say you want to ID the trailer, do you mean the type, or the individual identity of it?
The type of trailer is a Workshop/Platform trailer that was equipped in a range of various fitouts to accomplish specific mechanical support/engineering roles and used by RAEME. A limited number were also used by Artillery in rangefinding and radar roles. See
http://www.remlr.com/trailer-workshop.html for pics and descriptions. The trailer was introduced in the early 60's and shares a lot with the No5 GS trailer. The trailer you have has it original body and canopy frame, but the wire mesh and tailboard are later modifications or additions most probably done after it left the army. It also appears to have had the axle replaced with a civvy trailer axle with Landcruiser hubs.
For specific ID of the individual trailer you need to take the body off the chassis to locate the chassis number, which can then be cross-referenced to the ARN list to discover it's identity. That will then give you the description of it's original equipment configuration, and
might lead to finding and original picture of it in service.