I'll be honest, I don't know what C & C stands for, but it is basically a cage that you put together yourself using grids and connectors. She's just over 4lbs, and she's a little dwarf rabbit. (if you want to see it heres the link: https://www.guineapigzone.com/c-and-c-cages-guinea-pigs - no advertising intended :p)
It's hard to say if her head would fit through... but with the 1" spacing she can fit about a quarter inch of her nose through the bars to chew on them when she wants something. On the website for the one with the smaller spacing it says that 1 3/8ths inch is the safe spacing, but for guinea pigs not for buns. I can't seem to find anywhere what the safe spacing is for buns before I purchase
I've seen lots of videos on youtube of people who have purchased the grids from the same website and their bunny's seem happy, but I want to be sure before I buy anything.