I'm not surprised at the announcement or the rapid progression.
It could be in response to the embarrassment of stealing your underwear but I would think very carefully about supporting a social transition.
For example you will need to consider what will happen at school and if this new 'identity' means your child should use the girls toilets and change with the girls for PE. You mentioned a concern about stealing clothes from female friends, so you must be concerned about boundaries.
If your child requests puberty blockers please look at all the studies (and even the threads on MN) which detail the affect on bone density rather than follow what Mermaids and similar lobby groups insist is a safe 'pause button' (even Dr Polly Carmichael, head of the NHS Gender Identity Development Service, admits that this is not accurate).
Here is the Cass review
cass.independent-review.uk/
And perhaps also this
4thwavenow.com/2017/12/07/gender-dysphoria-is-not-one-thing/
There is much to consider and I would encourage you to do lots of research before proceeding too far as even socially transitioning can be dangerous. For me a child should always be able to change his or her mind and be told that even though they might feel a certain way or like wearing certain things you cannot change sex.
Your child will never have a period or get pregnant and the basis of this sounds very much like a sexual fetish developing from an early sexual experience, possibly porn, possible sissy porn, possibly influenced by online social media or even peers in school.
As the number of Detransitioners is growing and many talk about the speed at which they were affirmed and treated medically, inc surgery, I would urge caution and look at long term, unbiased talking therapy options.
fb.watch/5ShS0YILZz/
www.facebook.com/867420437/posts/10165279642945438/?d=n