Jenny makes what I think is the same noise when picked up. It used to be every time, but she made it less and less over time, and she has almost stopped now. Gina used to make it too. I think it is mainly objecting to being picked up, and both girls used to growl at me when I came close to them for whatever reason, but again, its seldom either do now. My guess would be that as she learns to trust you more, she will make these noises less.
I also think some bunnies are just more vocal than others. Pippi honks for food, but has never made the other noises, and so far I’ve heard nothing vocal from our new adoptee, Podge. Try just talking back to her e.g. when she squeaks, say to her, ‘Yes I know you hate me picking you up, but its only so I can carry you to the garden (or wherever you are carrying her)’ or ‘Yes I know its your toilet roll, but isn’t it fun to play together’, so she knows you’ve heard her!