Some useful stuff here about transitioning to a low carb diet on insulin
D-solve -- low carb and low insulin diabetes management
Dr katharine Morrison who wrote the How To's is a renegade GP with a Type 1 son
IMO it's perfectly doable with care, you need to have a good grasp of insulin ratios etc. and be prepared to shoot extra adjustments and gobble glucose tabs when necessary until you get balanced. Over time I've met several Type 1s who like Sam have enviable A1cs without hypos. Almost impossible on the Standard Diabetic Diet.