Hey, I don't mean to self-promote, but I wrote a post about my experience switching to the diet some time ago. I have been on it for the past 5 months and really saw an amazing improvement with stabilizing my glucose levels. I am currently switching to the pump, however I feel confident that I would be perfectly fine and healthy managing the T1 condition with just MDI and following this diet. As far as fat goes, you can get your protein through lean meats like chicken breast that don't have much fat, just stay away from the burgers.
https://forum.tudiabetes.org/topics/experience-switching-to-paleo-diet