Do they do endotracheal intubation?

Yes, but the risk for a healthy young female is extremely low. You should be more concerned about who is your surgeon and about the ability to achieve the results you are looking for, which I am sure you have done so far.

most anaesthesiologists would use an endotracheal mask for a breast augmentation. This is less invasive than an endotracheal tube. However it is something you would have to discuss on an individual basis.