Aww, such a cute bunny ^_^ Makes me miss the one my family had for a while, poor thing. One thing you might want to watch if she is bigger than the cat that she doesn't hurt the cat. Rabbits can seriously injure cats if they feel threatened at all, one good kick and it can be the end of the cat in fact.
However the bunny we had loved my cat to bits and used to follow him everywhere, while my cat was just like "omg, this is so embarrassing :/". Ooh and he loved dandelion leaves so if you have them in your garden they're great for treats
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Veggies are always good as mainly pellet based diets can lead to fat rabbits, so veggies as a supplement are great. Carrots and all the obvious stuff are great, cabbage is to be avoided though if I remember right. It's been ages since I looked after one though so I'm sure you know a heck of a lot more than I do!
Lovely name too *admires pretty bunny*