MOVING from San Antonio to Jacksonville thinking about respite care for husband while I go to look for apartment. Thoughts?

I would bet that most facilities are closed for Respite care at this time. And even if they were not I think he would probably be safer at home with someone to care for him while you are gone.
If the facility where he has been before is accepting Respite placement I would be very cautious.
When you return and pick him up place yourself as well as your husband in quarantine for a minimum of 2 weeks. Longer if possible, 4 weeks would be ideal. So get plenty of supplies before you pick him up.
It would be even better if you can postpone your trip for a while.

Called respite care, they said they will take him just have to get paperwork from dr. We have dr appt.
Thank you.

In my area no respite is being allowed right now.

You should check into the facilities current situation.

Best of luck with your move and may you find the perfect apartment.

Place him in respite care for both your sakes. First, do you really want to handle a melt down at the airport or on the plane? And second, finding housing when you are unfamiliar with a city is a full day's work and can take weeks. Enlist a realtor now to help you find an apartment, which will save you a lot of time. As you search for a place to live, you will not have the time or energy to deal with much else. COVID is what it is. There are risks everywhere. Your husband will be safer in the care of professionals.