How to get private Academic/Achievement/IQ testing?

Have homeschooled my kiddos for the past 3 years and just wondering if we've hit a ceiling with my oldest. I need to find out her potential so that we can adjust our expectations and not push beyond them. That said, I also don't want to cut her short if she's capable of more. The public school is legally obligated to test her IQ if we request, though they will use whichever test they want to and not one that will necessarily show us what her strengths are. (I'd like to learn HOW she learns best and teach to that.) I also need to learn what her potential is so that we can schedule high school curriculum accordingly. (She's 15, just finished "8th" grade, but currently working at 6th and 7th. I can't enroll her in 9th grade courses in the Fall until she completes 6th, 7th, and 8th grade in all subjects.) Anyway, does anyone know what type of testing I can request that will tell me what her POTENTIAL is (like how far she can go and, for example, if high school Algebra, Biology, etc. are even a possibility vs. just basic math, science, etc.? Of course since we're homeschooling, she can go as slowly and with as much "help" as necessary to master the material.) Also, is there a way to get any of the testing covered by insurance? Mine have Medicaid as secondary, and our primary won't cover "academic testing." They did cover her initial psychoeducational? eval as a followup to a RAD and ADHD diagnosis. That score was 73, and it's likely where she is today, though her grammar has improved a great deal and she seems much more "with it" then she was when she first joined us 8 years ago. Thanks so much for tips!