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How the starting dose of insulin is determined can vary based on the insulin and what dosing method you're following. There are a number of insulins that vets prescribe. However, the only insulin that is recommended by the American Animal Hospital Association is either Lantus (glargine -- Lantus is now available in a generic/biosimilar) or Prozinc. Other insulin such as Vetsulin (also called Caninsulin) is no longer recommended due to its short duration and harsh method of action. However, in some countries outside of the US, the vets are restricted in what they can prescribe.
We also recommend that you are home testing. If you are not already doing so, we can link you to information on how to do this. Most of our members use a human meter since the cost for strips is far less than with a pet specific meter.
It would also be helpful to know what you are feeding your cat. Many of the prescription foods are actually not low in carbs.
Also, are you sure the weight you noted for your cat is correct? We tend to use pounds and ounces (most of us are in the US) and 6.9gr is only a few ounces.