this is from SWA's site:
Although one might think that any type of restraint device would provide at least some degree of flight safety enhancement, this is not the case. Some child restraints may do a good job of protecting children in automobiles or in other situations, but are not appropriate for aviation use. Recent testing and research have led the FAA to ban the use on aircraft of certain types of child restraints that may be harmful to a child in the event of an aviation emergency. These include booster seats, safety belt extensions (commonly referred to as "belly belts"), and vest or harness devices that attach to an adult or to the seatbelt of the child's own seat. Although some were manufactured before the FAA's ban may carry an insignia and/or language indicating they are approved for aircraft use, please understand that they are no longer permitted.
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From this I get the impression that boosters are not permitted.