I think she'd be as protective of her as she is of Henry

Although, she might be slightly more protective of Henry. For some reason, mothers are usually more protective of their sons than they are their daughters, just like how fathers are usually more protective of their daughters than they are their sons. I guess it's because they've been in the same situation as the child that is the same sex at them.

Also, didn't you already ask this question?

^There are several polls on the same theme asking if she'd be softer with a daughter, and asking if we'd prefer her to have a daughter or another son, but I don't think this one was asked before.

She'd be more protective of a younger child because of the age, but I don't think she'd specifically be more protective of a daughter. Maybe she'd also be more protective of her own child than Henry because her child would only have her and possibly the child's father, while Henry has his entire biological family too.