It's very bad for diabetics to be eating bad fats (LDL's) which come mostly from dairy fats. Concentrate on getting your fats from HDL's (olive oil, avocados etc...) or you'll give yourself heart attack cholesterol problems to add to your diabetes one. I highly recommend a Desmond (diabetes) course for everybody where you'll learn all this stuff!
I'll join in here Junius, with a book recommendation too - this one has includes fantastic references, and she spells it all out very well - Nina ‘Teicholz's 'The Big Fat Surprise: Why Butter, Meat and Cheese Belong in a Healthy Diet’. Naturally I'm including full-fat yoghurt in the healthy fat foods here!
And take a gander at her webiste - ninateicholz.com.
Junius, I know it's a strange turn around on dietary recommendations, and very very hard to get your head around the bs of dietary fat, especially that animal products is bad for us - it was the first thing I had to do when I changed my diet to low-carb (and I was only moderately low carbing at first). It was so weird for me that I used to laugh as I added butter to the pan, and learnt not to burn the coconut oil, that I was using these fats that I had been told would kill me. Boy was I surprised to find out that theory was never proved, and has since been disproved! I see why Teicholz named her book what she did - surprise is a good word.
But here you are in the low-carb diets section - and when you lower your carbs, it is recommended that you up your healthy fats. And, healthy fats are not what we were told in the late 70s on... anyway - read the book or her website, and yes Kendrick too...