Congrats on your new adventure-mobile! You can flat tow a Toyota Camry, but only if it’s equipped with a manual transmission. The manual transmission was only an option from 1992 to 2011, so if you have a car newer than that, you have an automatic transmission Camry.
In this case, you have two options. If you have a front-wheel-drive Camry, you can use either a two-wheel dolly or a flatbed trailer. If you use a two-wheel dolly, make sure the front wheels are lifted off the ground. For AWD Camrys, you can only use a flatbed trailer to tow the vehicle.