Make sure your car insurance covers all passengers and in UAE as well. Check with your insurance company.

Getting a visa is the preferred one. Don't attempt at entry point.

Keep on attempt in UAE embasy in Doha (Diplomatic area). I got in fifth attempt 8 years ago and I travelled in Honda civic (1994 model).

Going by Carolla is not bad.
Drive safely with in speed limits.
UAE border to Abudhabi road especially after Ruwais look-out for sand accumulation in the main highway itself. Keep very close watch.
Every 200-300Km give rest to your self and car 10-15 min will do.

Get a decent street map of UAE in order to not to get lost in looooong waiting traffic jams. Plan and drive. Avoid rush hours.

Enjoy