I just did this a few weeks ago with our new 560. In theory they don't need to look at the trailer, but they insisted and I didn't have the energy to argue with them. They did an inspection of the trailer, starting with "what is this?". It doesn't fit in well with their categories, but finally the inspector called it a "camper" - makes sense to me. She did write down some stuff from the VIN plate that is not on the form they gave me to fill out, but it is not clear to me this is really needed.
It was actually pretty painless, except that I made an appointment for the registration, but apparently the inspection is not part of the appointment process. I waited only a few minutes for the registration agent, but only after spending an hour waiting for and doing the inspection.
By the way, in California, at least at the DMV, permanent really means 5 years. You have to renew the registration every five years.
If you paid sales tax when you purchased your 560, be sure you get that deducted from the amount the DMV assesses. This includes out of state sales tax.