Hi Saph,
I agree with M2C. My numbers were in your kind of ball park and I got to the same point in thinking that I had nothing going on. I was desperate to get an early scan and I think it was 5 or 6 weeks when I got my first scan and saw the little heart. It was an amazing experience and one I wouldn't want to put off and wait for. The doubling is only reliable to a certain point and even then, it's not a daily double, it's more like every day and a half when it's happening.
I think it is routine for girls to have the scans done earlier. We are the ones freaking out. Waiting for a calendar date is fine in theory, but murder in practice.
I don't know anything about ectopic but I hope you get some answers and an early scan to put your mind at ease.
Chin up, we'll be thinking of you.