The key difference is that you can plan an exact day for your flight well in advance but you cannot do the same for your car’s pick up or drop off. On average carriers book their loads only 1-2 days in advance while the optimum time to book a flight is 54 days in advance according to this study. A back up plan is a necessity. You can allow the car to be picked up early, you can have a friend or family member release the car to the driver after you have gone, or you can put the car in storage after you have gone. You have to create flexibility.
Another option is to pay a high rate. Paying more means a carrier will book further in advance. It won’t be a week but 4-5 days is a possibility depending on how much more you are willing to pay. If you are in a rural city however, you are just going to be waiting for a truck to come through your town. You will have to pay more and you will have to be accommodating.
The best thing you can do is to let your broker know as soon as possible what your plans are. Planning a flight around when your car gets picked up isn’t a good idea. You will pay extremely steep rates if you wait until the last minute to book a flight. Pick a strategy that works for you. You could even get lucky and have a carrier move your car on the perfect dates, just make sure to have a plan B.