I carry Cali through security and they use a wand on her and me usually. The carrier has to go thought the X-ray machine.
You can ask them to assign you a seat that has the greatest room for your carrier.
Your carrier will have to have a top that zips closed to assure the dog stays in the carrier (if it is not a service dog).
We travel a lot and have never been refused a ticket based on the type of plane, but things are always changing with the airlines.
Good luck, hope it is an uneventful trip