Oh, how heartbreaking for you to lose your baby, I totally understand how devastating that could be and how it would make you nervous and extra careful with your next baby. I just got a bunny a month ago and became very protective of her right away. I have found this website and rabbit.org to be invaluable for diet and health information.
This link gives some info on bunny babies that might be helpful: http://rabbit.org/category/care/babies/
and this link specifically discusses diet: http://rabbit.org/category/care/babies/
I also purchased the House Rabbit Handbook and it’s a GREAT read! Everything you need to know is in there.
My bunny is a little bit older than yours; I introduced greens and fruits at about 8 weeks. Just a small amount to start, as everything I read indicated that their diet should be mostly timothy & alfalfa hay, then pellets, then veggies with fruits just as a small treat. So I usually give Hazel about 1/4-1/2 cup of veggies with one small piece of fruit twice daily and unlimited hay & pellets (and of course all the fresh water she wants). Also, my baby has been eating on a willow house since about 7 weeks old and has been okay. They say that carrot has a lot of sugar like fruit, so I always treat the carrot as a treat and have the mixed greens be the bulk of the veggies she gets. No iceberg lettuce – not sure if it’s because it can make them sick or just because it’s pretty much useless for nutrition.