Keep in mind that food basically consists of three "component groups": protein, fat, and carbs. Carbs are a catch-all group- sugar, fiber, alcohol, starch, etc. Low-fat and low-carb basically means you will be eating a very high-protein diet. That is definitely not a rabbit diet.
Also, I'd question how old the dietary information is that your doctor is using. The body produces cholesterol naturally. The contribution from your diet is so small and its effect has been disproven so thoroughly that the US government has finally removed it's recommendation to lower cholesterol via diets.
New US Guidelines Will Lift Limits on Dietary Cholesterol
Yeah, I don't think my doctor is up to date on the cause/effect thing with animal protein and cholesterol. I was going to a doctor who was a serious proponent of high fat/low carb, but I switched because I could never get in to see him. I may go back to him for dietary and weight issues and keep my present doctor for when I have a sinus infection and need to see someone sooner than a month out.
This is the doctor I used to go to and will probably go back to. He's arrogant, but he's a great motivator.
[video=youtube;sfvdJVrQ1ZA]https://www.youtube.com/watch?v=sfvdJVrQ1ZA[/video]