Yes, it will depend on the personality of the rabbit, too. Also, getting her spayed after she’s definitely 5-6 months old will be a very necessary thing to do — it will help her attitude, but it will also prevent her from getting reproductive cancers.
I think the biggest differences are that dogs sort of look to please you, a lot of the time, and that alone can be their motivation. They’re all about you. Cats are more all about themselves, but they also love you, too. Unless the cat is extremely aloof or feral or something. xP With rabbits, it’s sort of like… they’re about your relationship with them. I have no idea if that makes sense. But they’re extremely aware of how you behave around them and therefore how they respond to you, and vice-versa. They’re extremely social but not quite as prone to being affectionate and outgoing by default like dogs are.
But that is definitely not to say that they can’t become just as affectionate and loving as dogs! But it’s just usually a different kind of affection, I suppose. And keep in mind that it can take a while for rabbits to feel totally comfortable in their new home. It took Theodore 3-4 months before he felt he was finally at home here. So just keep patient!
Spaying will definitely help.