Actually; I fear the OP is right to expect that her DD will start to identify as trans the moment she gets on tumblr, or is told about it by her peers.
When I was 7 I told boys who claimed my haircut was a "boy" haircut to fuck off. (Ok, not really, but I distinctly remember thinking them very silly. Not sure what I actually said at the time)
Actually getting to the point where you wish you were a boy instead of wishing you could crush patriarchy, is rather dangerous nowadays.
Others already said all there's to say about not doing any gender stereotyping to the child.
I only have to add: Tell her about second wave feminism. There are no feminist texts for 7 year olds, as far as I am aware of, but you can read stuff and tell her about it in an age appropriate way.
Show her that she has a choice. She doesn't have to be transgender. She can also become a feminist.
The thing is that nowadays, as gender non conforming girl or young woman, you either become a feminist or you succumb to the extreme pressure of transgenderism.
If you encounter transgenderists in your life, and in the UK, you will, they WILL force you to call yourself "cis" and thus pretend that you identify with being oppressed under patriarchy, and chose oppression, or pick some of their approved gender identities.
If you resist them, you don't even have to consider yourself a feminist. They will call you a "terf" thus decide it for you.