My 7th grader (then 12) took an algebra readiness test at the beginning of the year when she was still in the 7th grade math --- it showed a high enough score to be ready for algebra even then. There were some gaps that the test pointed out, but not too many.
We used the readiness test with her Stanford 10 math scores to push for algebra this semester and got it. She has had solid high A's this whole semester. We met with her Algebra teacher after a few weeks to check in and I asked about any gaps --- she wasn't too worried.
If you can get the readiness test in your state, then definitely get it. If it shows your child's ready for algebra, that's one tool to help push for it. If it shows significant gaps, at least you'll know what they are.
In my little school district, gifted kids get what the school can feasibly offer. Meaning if my elementary kid needed algebra, it would not happen. However, since the middle school is on the same campus as the high, sending my DD over to the high school for algebra was do-able. I wish you luck!