Unfortunately, that probably is very close to the actual shipping costs. Despite what many consumers believe, there is very little discount on ground shipping through most of the major carriers, even for business.
Car seats tend to be loss leaders. Even though a seat may cost the end consumer $300.00, the take home for the business could be a little as a few percent. A $300.00 seat may be almost $200.00 wholesale. The mark up is 50%, but the unadjusted net is only 33% ($100.00 on a $300.00 sale). Now if you factor in that it can cost 10-15% of the base price of the seat to ship it into a store ($20-$30) and up to $55.00 to ship a seat across the country, the end result may be only a Net to the business of $15.00 on that $300.00 dollar sale.
Now assume that there is a 3% merchant fee for the privilege of accepting a credit card, which amounts to $9.00 on that $300.00 sale. The take home is now only $6.00 for that $300.00 seat.
All of this assumes that you have no overhead to sell your seat (i.e. employees, bank charges, phones, lights, internet costs, website maintenance, etc.). Tying up large amounts of capital into car seats is painful for all but the largest of stores. Given the above, you might invest $6400 to make $192. Granted, that is the worst possible case.
I suspect free shipping on car seats will soon be a thing of the past given the high costs of gas and continuous price increases for raw materials. Business won't be able to offer shipping deals on car seats, that many consumers have come to expect as standard.