[tevake]

Nope, it should tow OK with what you have for now.
The equalizer hitch will help distribute the tonge weight more forward in the tow vehicle, avoiding the sag at the rear. Keeping the TV. More ballanced.
Some of the modern hitches also have a side to side dampening function. Keeping the trailer from wagging the TV in side winds and when being passed by big rigs on the highway and in cross winds.
Trailers do gain weight as they get loaded for use, adding to the benefit of better hitch setup.

My Brothers rig, ford F250 diesel, 31' classic (heavier model ). Would really move sideways with the air coming off of passing big rigs. But is now very comfortable with his new hitch, I drove in N M recently on a trip with him in strong cross winds 30/45 gusty blowing tumble weeds kind of winds. With no problems, quite settled actually.

They are not cheap but depending on planned use may be worthwhile.

Endless threads on tow vehicles, hitches, etc on airforums. Wide range of opinions .

Trailer from the era of yours are lighter than newer ones, so can do with less serious tow vehicle. You will know a lot more by the time you get to the warm S. Ca.

Most experienced RV towers do talk a lot about keeping the speeds down around 60/ 65 mph for driving comfort and fuel economy.

I find going too slowly in fast trafic uncomfortable, so around 68/70 seems to be the sweet spot in my motorhome. It is around 65mph in my bro's rig.

You might want to start out on the slower side to get the feel of your rig and how the trailer handles on the highway. Have someone check if the brake lights are working on the trailer.

Just a bit of getting used to driving a larger rig. I've gotten quite comfortable with mine now, except for in crazy traffic like around SoCal . Folks there just don't leave gaps big enough for longer vehicles to merge into. No mercy there.

Cheers Richard