Technically, <13 y-o are allowed to take the SAT, but not to register for them online, or take them at any nonstandard administration date. But yeah, it would be simpler to just wait until her birthday!

I've had my young teens take the SAT at around this age as a reference point for myself (especially as each of them was homeschooling at the time of their respective tests), and so that the first time they sat for it, it would be very low-stakes. Good thing, too, since one of them failed to turn the page at the end of a section, resulting in an artificially-lowered reading score! One set of scores also turned out to be useful when we started dual enrollment not long thereafter, and the school was willing to take SAT scores for placement.

For the younger child, any scores 8th grade or earlier will be deleted on high school entry anyway, unless you actively request to have them retained. For your older child, I personally wouldn't worry about effects on uni admissions, as I think most schools routinely superscore. And it might be a nice practice test for the PSAT/NMSQT (technically in reverse, I know!).

Also, I really doubt his score will go down between now and senior year! smile
...pronounced like the long vowel and first letter of the alphabet...