Based on this chart, your levels seem to be in the normal (towards the high end) range for 6 weeks' gestation:
https://americanpregnancy.org/while-pregnant/hcg-levels/
This site is also very useful in explaining things:
https://www.babymed.com/hcg-level-in-early-pregnancy
One important thing is, your levels will most likely NOT double every 2 days at this point ("Above 6,000 mIU/ml, the hCG often takes over four or more days to double", per the article), so as long as they go up, this is good and normal. If your doctor tells you otherwise, please don't let them scare you - ladies post here every day who have been told bad things by doctors just because their levels didn't double while at a later stage, and most end up being ok. As long as your levels increase at this stage, you're probably fine.
Also, ask your doctor if he/she can give you a scan. You should be able to see a sac/yolk sac at the very least at this point and with these beta levels, and possibly even a tiny embryo with heart beat. The article also says it somewhere that ultrasounds are much more reliable than beta levels after a certain point.
Good luck, keep us posted!!