We also don't live close to any private clinics that offer ultrasounds. In fact, my doctor's office (which is only 10 minutes from my house) doesn't have ultrasound equipment either. I have to go to a satellite office approximately 40 minutes away... and none of the private clinics that I've found online are even THAT close. Such is the life of living in the mountains.
Argh that's a shame. But as you said, you will find out soon anyway even if you can't get a private scan! X