Keep the Fl plates, registration, driver's license as long as you can. If you don't have to get an inspection in Florida and just have to send them your payment to renew, keep the plates. Fly back to renew the driver's license, if you have to get a picture taken. Keep the less expensive Florida insurance (if it is cheaper).
If you want to go through the hassle of doing the change right away, smog testing shouldn't be difficult. Probably best to establish residency first, then smog. If you don't/can't pass go to a gold shield testing station, go through the process and have the state pay for your smog repairs. Since you haven't really modified the car, put on the original AAV, smog it, pass, change it back. Or, not that I'm saying you should, find a place and have it passed.
I wouldn't worry about being pulled over for out of state plates, especially in LA/Hollywood. SOOO many cars around here with out of state plates, obviously current Ca. residents (Arizona, Alaska, Hawaii, New Mexico, Arizona, Nevada, Illinois, Georgia, Texas, Florida... to name a few). This all changes if you get a ticket etc, but if both plates and license are still Florida probably not (since you're just visiting). I kept my old plates for about a year. Don't get the new license until you have found a place to live that you're happy and comfortable with. Pain in the butt to have to change your address on the license if you move after a few months.
Get Trapster for your Iphone or whatever mobile phone you have. It will show where where most all of the redlight cameras are (watch the the little crosswalk guys for the countdown, so you don't get hit with an outrageous ticket). Don't worry about all the helicopters, you'll get used to them at night. Don't be surprised when asked about the earthquake or fire in the LA area, that you have no idea about, by someone from out of state. Its a fairly large area, and you either won't see the fire or have felt the earthquake (you may see the sunlight change to an orange color and see or smell the smoke, doubtful though). Do keep a working flashlight and a pair of shoes by the bed (for the earthquakes and broken glass).
Btw, it was easier to use "you" for both you and your son, then go back and correct everything.