I'm not eating a lot of fruit at the moment, although I'll add some back in gradually once I reach my goal and am maintaining. There's a pretty good list of veggies in Doug's book and a lot of them are low carbs. I'm not drinking milk right now other than almond milk. It's carb-free and I love it, so that's been a great new addition for me. It is only 35 calories per cup, which sure beats the regular 70 in other milk. Jimaca is a great alternative to potatoes if you like that sort of thing.
I hope you can make this program work for you. I don't know much about vegetarian diets, but it sounds like Doug & Umpa are willing to help you along, which is great. Cutting out the sugar is just what I needed in my life. Now that I look back, so many of my problems have been sugar related and not just about weight -- my teeth especially. I can't undo the damage I've caused them, but at least I can work on all the other issues. My next step is getting off this stupid high blood pressure medicine, which makes me really dizzy whenever I stand up fast. I hate that.
Good luck and I will keep my eyes open for veggie ideas for you!