Also, generally speaking, is it better to get a B in an advanced/challenge program than it is to get an A in a standard course?
I wouldn't worry too much about grades - there are variables that go into grading that have nothing to do with the challenge level. Instead I'd focus on whether or not your child is learning anything in the course they are in, are they learning at a rate they are capable of or do they complain about the pace of instruction being too slow, are they saddled down with a lot of repetitive classwork and homework or just the right amount to be learning and moving along? Those are the questions I'd consider re correct placement. I'd also look at things such as quality of instruction, teachers, philosophy of program etc - moving into an "advanced" program doesn't always directly correlate with learning more or a better educational experience.
In your situation, the first thing I'd do is learn as much as I can about what criteria is used for placing children in the advanced math track (and learn as much about it as you can). Once you've got that info, try your best to fill in what your child is missing in terms of data (testing, other requirements such as teacher recommendation etc). If you can't get the placement you're looking for with the info the district/school is looking for, ability testing (IQ) *might* be helpful - we've used it as one data point in arguing for acceleration for our kids. It can be expensive though, and it will always be just one data point (which is usually looked at along with achievement testing, state testing, teacher recs etc). IQ testing isn't always looked at as something worthy of considering either - we've found some teachers and school staff to be very dismissive of it, so I wouldn't recommend assuming it will be well-received.
Whatever happens with this decision, I'd also not take my eye off the future for advocacy - we weren't able to accelerate our kids in elementary school but it was much easier once they hit middle school and math courses were more, er, straight forward. Our elementary school curriculum spiraled and included a lot of word problems, feel-good stuff for folks who don't "get" math, that type of thing in addition to nuts-and-bolts arithmetic. Once we were looking squarely at pre-algebra, algebra, etc it was much easier to prove achievement and ability and get a proper math placement.
For now, re after-schooling or enrichment (which we did for the two of our children that subject-accelerated in middle school) - stick with something you can tie to your state curriculum standards. Don't pay attention to things like curriculum standards in other states, or state testing. As someone mentioned above, it doesn't take much to score "advanced" on most state testing - in our state, I'd guesstimate at a minimum around 20% or all kids are scoring "advanced" in elementary school. Plus state testing doesn't go beyond grade level curriculum. MAP testing does, so keep your student's MAP scores. OTOH, don't be surprised if there aren't other kids in elementary school also scoring high on MAP - and don't be put off by being required to have something additional in the way of data. It doesn't mean your child shouldn't be moved up, it just means sometimes with advocating you really have to build a case for it. I hope I'm making sense!
Re IXL, I haven't seen it in years (my kids are all out of elementary school now), but I think it does have a tie-in to state standards. So check that - can you show what your child has mastered in IXL in a report that ties it to *your* state standards. If so, run those reports and keep them as data to show to the school. We did this with ALEKS when we after-schooled and it was a really easy way to show the school how what our kids had mastered tied directly to what the state/school district was expecting them to master at each grade level.
You can also ask your school to administer end-of-year exams for upper grades to show what your child has mastered - at least in theory you can. Our school district didn't have those when we asked
Best wishes,
polarbear
