Hi,
@amelia98 , I wouldn't worry about 0.6.
We've all got some ketones swimming around normally and that level isn't putting you in any danger.
If you have a look at the NHS guidelines, link below, they say lower than 0.6 is nothing to worry about, 0.6 to 1.5 is a slightly higher risk but they're not talking about calling an ambulance or anything like that, just test a while later to see what's happening.
We can't advise on whether you should take insulin or not as we're not doctors and don't know your full background, but, having said that, you probably know that 9 is higher than the preferred 4 to 7 range, so you should maybe think about making a judgment call on whether you should take a unit or two to nudge it down.
If you've still got active insulin on board from your last bolus, maybe that'll bring it down on its own as part of dealing with your last meal, but if it's been more than about 4 hrs since your last bolus, a little shot might be a good idea to bring it down. Or if you're planning on a meal soon, maybe just save it till the meal and add it on as a correction.
Ketones are really only something to worry about if you're running around at really high levels for ages and not bothering to take insulin for meals.
https://www.nhs.uk/conditions/diabetic-ketoacidosis/