Shipping luggage?

I am moving to California from New Jersey and I will be driving there. Me and my daughter have so many clothes they just won't fit in the car. I am not using a moving service because I am not bringing any big items with me and I have three full sets of luggage pieces so I was thinking of shipping our clothes and other personal items in those. I noticed Fedex, UPS, and the Post office all ship luggage. I was wondering if anyone has ever done this before and how much it cost them? The items are not time sensitive. I will be shipping them two or three weeks before I move and most of them I won't need right away. Thank you for your time.

If you are going to drive anyway the cheapest way might be to rent a car top carrier from a place like U-Haul.
I ship boxes for my work through all the carriers you mentioned and it gets pretty expensive. It is really impossible to give you an estimate since you don't say how much you will ship. All those places have web sites where you can get prices on how much it will cost to ship a box based on size, weight and destination.
Another option you might try when you know what you are shipping is http://www.uship.com/ . I have gotten some very good prices bidding jobs through there.

From Chicago to Los Angels, I used UPS. 2 boxes (20in x 20in x 20in) filled with my clothes. Chose 3Days shipping, not ground shipping. Then the total amount was less than $400. I am not sure cuz some years ago. Also depends on the weight of boxes and the distance.
I hope this helps.