Are you willing to make the trip at no more than 55 mph?

 

I would get a quote from an auto transport broker and weigh the costs.

You're going to be right at the max towing weight if not a little over (depending on what year Corolla), which is never a good starting point for a towing journey. Also, like @xGS said you are going to have to take it slow, so figure the extra days of hotel stays. Also the cost of going cross country while getting 12 mpg.

Professional haul service will probably only be $500 or so.

 

I had a car shipped from Arizona to Ohio last summer, it was more like $3000 to have it shipped, although that was for enclosed transport since it was an antique. A quick look at the FWD towing capacity for a 2025 Pilot is 3500 pounds, and the weight of a U-haul car dolly is 750 pounds. Looks like a Corolla is in the neighborhood of 3000 pounds. When I had considered moving this antique car myself, I looked at using U-Haul's car transporter (flatbed), which was about 2200 pounds. When I put in the car and my pickup truck's specifications, U-haul's website pretty much said NOT RECOMMENDED, since it would be right at the limit of what my truck could do. You might want to try U-haul's website first and see what it says.