If you think kava is worth a shot for her, it might be worth trying an instant and putting it in capsules for her to swallow. This has the added benefit of easily producing duplicatable results in case she has a positive reaction. I'd think instants made from a processed kava drink would be better than a micro just in case she has stomach issues from the fibrous materials like so many adults experience, would be the better choice. Or maybe even something like KWK's relaxation drink might be worth a shot if she enjoys fruit flavors. Folks on the spectrum are often extremely picky eaters and frequently fixate on texture and mouth feel far more than the flavors most neurotypical folks look for first so I don't know how well that would work, but it's something to keep in mind. There are other potential options for kids with issues like this, some of them better studied. Things like phenibut, l-theanine, and maybe even a quality bacopa extract could all potentially be of some help. Beta blockers are mild blood pressure meds often used off-label for extreme anxiety and phobias (usually in conjunction with therapy, of course) that alter the way your body processes stress at a very fundamental level, so it might be worth mentioning them to her doctor and seeing what they say. Melatonin is probably the best OTC sleep aid in existence, but it's also famous for causing very intense dreams, so just keep that in mind if you try that.
Having said all that, I'm definitely nor saying I recommend any of those things. All kids are weird on their best day, and having sensory issues and discussing potential treatments that aren't very well understood even for adults could cause unforeseen issues for them that most folks won't have to deal with. Autistic people can process many things very differently than neurotypical folks do, so it's honestly kind of a crap shoot regardless, even if she wasn't so young. I've spent a lot of time with folks on the spectrum to varying degrees and it can definitely be difficult, but I couldn't imagine having to go through something like that with my child. Best of luck to both of you, regardless.