Dentist and pregnant

So, I'm 26+5 days right now...and awhile back I needed to get fillings done, however every time the appointment came up I would suffer a bout of morning sickness and it was great. So...I had to cancel and finally just decided to postpone until after pregnancy. However, I have a cleaning I think on the 16th and my teeth ate beginning to bother me once again and I know I need these fillings...my question is, is it still safe for me to get cleanings/fillings done while pregnant because I know I'll be on my back and after a certain while they say to not be on your back.