Hi there and
to the forums!
I agree that the feathers coming off as they're being grown in could be a sign of french moult. Photos would help for sure, if you're able to post some from Photobucket or the like.
It could be normal, however, depending on how the feathers are falling out.
If "she" has a smooth, pearly, pink nose, then "she" is actually a he!
Behaviour tends to not be the best identifier of gender, as all budgies can have different personalities.
Meanwhile, be sure to read through the forums as there are lots of good links here that may help you with your little Trix. Any time a budgie looses feathers, whether through a moult or French Moult, a high protein diet is great for helping their feathers grow in as strong as possible. Mashed hardboiled egg, as mentioned by Pretty Boy, will help her with that, if she'll eat some. If not, flax seeds are a good alternative, and they are more familiar to her in terms of shape and size
I hope everything turns out well for your little one! Please be sure you keep us posted on how Trix is doing
If you have any questions after reading through things, be sure to ask as we'd love to help!