She didn’t say she was going to the dentist. She said she had an “appointment” and needed to check she had the letter (so unlikely to be dentist). She just asked Jamie, hyperthetically what he would think of first if he had a [dentist] appointment. I think she just used dentist to make her question more specific for him (otherwise he would respond with “what sort of appointment?”).
A dentist probably wouldn’t sent an appointment letter and if they did it would be sent far in advance, which is unlikely considering the current situation. She’s got a hospital appointment - perhaps a scan, which is probably what she wants everyone to think, except we didn’t.
Oh and Ronnie (and presumably Jamie) are going too. They wouldn’t all need to go to the dentist.