It's unlikely that you'd be able to find an exact replacement, so some careful measurements should be all you need. The enclosure is probably attached to the stud-walls, so figure it is nominally 1/2" bigger than the dimensions you can measure (i.e., it probably extends 1/2" beneath the drywall that is usually used in the room around it). Some have a flange that is covered over by the drywall, and you'll have to remove some of that to tear out the old one.
The drain on an older shower might be 1-1/2", and pretty much all of the new ones will be 2". Talk to your inspector if this is the case, as he might allow you to use a 1-1/2" drain, but also might require you to update it to 2". The shower valve on a really old shower is unlikely to have anti-scald technology, so you'll want to upgrade your valve at this time as well as maybe the shower head (2.5gmp max). finding one that gives a good feel is tougher at this flow rate, but possible.