Go for the backless! Really, as I've said before we'd all be safer riding in 5 pt harnesses, but how many of y'all have them for yourselves? You can buy them aftermarket and have them installed in your vehicle, y'know.
My dd1 is 7.5 and about the size of OP's dd. We just switched her over to a backless. She went on a field trip in another parent's car and was thrilled to have the back off her booster. It's a Graco, so we can take the back off and put it back on when we want to. We may put the back back on for sleeping comfort on long trips. We do have a vehicle that has side curtain airbags and that helps me feel better, but it is probably not the most absolute safest vehicle ever made. (It's a VW Golf ftr.) If you get t-boned by a semi not sure a tank would help, y'know?
You take some chances in life. Just riding in a car is a big chance, so is crossing the street or going swimming or taking a bath. Take some reasonable precautions and move on.
IMO, the OP's daughter is not that small, either. There are plenty of kids in that range in my daughter's class and amongst her friends. I think dd1 weighs about 45lbs and is probably about 47 inches tall. She doesn't seem especially petite compared to her classmates although she probably is more slender than quite a few of them. I was 42lbs in the second grade and I am a completely medium grown-up (5'5", 130lbs).
In our state (NC) the law is 80lbs or 8yrs old. Most all of the kids in her class are in no back boosters. There are a few who are really big and probably don't use boosters at all and at least one pretty petite girl, but she uses the built in booster in her van.
So that's my 2¢.