As I understand the rules, any DOT approved child seat is OK
in an airplane for an appropriate sized child.

Its a bit more specific than that. When my boys were small there were
only 2 seat manufactors taht met the requirements.

91.107(a)(3)(iii)(B)
(2) Seats manufactured to U.S. standards on or after February 26,
1985,^M
must bear two labels:^M
(i) "This child restraint system conforms to all applicable Federal
motor^M
vehicle safety standards"; and^M
(ii) "THIS RESTRAINT IS CERTIFIED FOR USE IN MOTOR VEHICLES AND
AIRCRAFT"^M
in red lettering;^M