As far as I know, Mears neither requires nor provides car seats (FL law does not require them to be used on "public" transportation).
That said, I urge you to bring your own. Most airlines will allow you to purchase a seat for your infant at half price. Your baby will be safer and more comfortable in his/her own car seat. If, God-forbid) something happens (air turbulence, traffic accident, etc.), you will be very glad you put your precious child's safety above saving a few $$. Best wishes - enjoy your trip!