First, I would encourage you to drop the words "big girl" from your vocabulary.
You are wanting her to be more mature than she is, because she may be feeling like she has no 'spot' of her own. She obviously doesn't want to move from the crib, but I wouldn't have included "baby will be using the crib" in that conversation, just "now you are old enough for a real bed", period. I'd also take a break on mentioning the baby for now. This is an enormous new unknown for her. (Think about all of the moms on this site who had a hard time transitioning their little ones from the crib to the toddler bed, without the added stress of an unseen-yet-considered sibling....this is very normal behavior.) She doesn't understand how much her life is about to change, but already changes are being forced upon her. She needs to grapple with these already-challenging changes on her own without the added element of 'well, grow up, sweetie, because you don't get baby status any more'.
I'd change the language to calling her Baby#1 and Baby#2 can be in the womb. She needs you to let her feel little, still.
Please do not compare how your son did in this situation to how your daughter is doing. They are two different people. She may want to help, or she may want a baby doll to do some 'parallel' caregiving play to what you are doing with baby. That, to me, would be a more neutral inclusion of your daughter at her own level of ability. Older siblings run a range of emotions when a new baby comes.
Personally, I'd consider moving baby's crib to your own room in the first few months. My own rule, when I was a nanny, was to never leave two young children alone together unsupervised.Even if I had to go to the bathroom, I'd put baby in the crib and have the older child in a different room playing. At these ages, leaving them alone together is not smart. It's very easy for a young child to unintentionally hurt the baby (even bringing too many stuffed animals to the crib, etc.) If it were me, I'd move that crib into my own room, because I'd want big sister to sleep well AND I'd want to know that baby was safe. That would be my own solution.
I should add, too, that in my time working with children, I often see the most stress and upset from children when their parents are actively trying to 'prepare' them for something. Here's why it is often a mistake: children do NOT think the way we do; their mind's don't work the way ours do. They live in the present and any situation they have not yet personally encountered is only abstract to them, therefore, unreal. They don't have the base of knowledge to draw upon that we adults do. I have seen parents do this time and again-- they 'talk up' something (new preschool, moving, kindergarten) and the child, instead of being reassured, is upset and angry. They aren't being allowed to just stay in the present (which is their norm at your daughter's age-- ALL she knows is the present) and then the parents are asking them to understand something they have never experienced. So, to most well-meaning parents, trying to do transitional work ahead of the game seems reasonable, but to the child it is a giant imposition upon their sense of peace and being accepted 'just as they are'. I hope this explanation can help you perhaps understand your own daughter's possible perspective on this. This isn't just my observation over 20 years of working with kids, either, it's an observation you will find in a lot of child development text. Your little girl is just fine!