MN started me thinking about this issue; I've read this thread and other 'trans' threads with interest. Learned a lot. Thanks MN. Some of my thoughts, written to clarify for myself as much as anything. It does seem important.
I have pre-school grandchildren, boys and girls. The older ones among them know some important and interesting (to them) differences between boys and girls, men and women; to wit, boys/men have penises, girls/women have vulvas. The older ones among them know something about how sex works; to start children you need grown-up vulvas and penises, hence women and men. All that is part of satisfying childish curiosity - part of development, if you like. (They don't all call them 'penises', btw.)
My children and their partners (these grandchildren's parents) are sufficiently sensible (my judgement!) to have made some attempts to shield their children from societal pressures to gender things like toys, clothes, behaviour etc. These attempts are based on the view (partly gained from their parents, we pride ourselves) of gender in that sense as likely being detrimental to proper human fulfillment ... to be more specific, perhaps, as being a mechanism for patriarchal control of, and discrimination against, girls/women by boys/men.
As a result of this shielding, my grandchildren could not possibly make any sense of the idea of 'transgender'. OP's 'Jenny', should they come across this older child, would simply be a big boy.
Now, of course, these my grandchildren can't be isolated from society as they grow and develop further. And our society, in the large, has notions of gender that my children (and their parents) think of as a pathology. It's a bad thing, we think, that girls/women are so often and so ingrainedly treated badly by boys/men ... and 'gender' being a constructed notion that helps enable such bad treatment, the very idea of 'gender' in this sense is also a bad thing.
So what's happening now in society at large? Here's where it gets tricky. There's a move afoot to reify (or possibly hypostatise) gender, so as to try to give sense to the idea that my grandchildren have some innate aspect to themselves that is independent of their boy/girl status as they currently understand it. And, lo and behold, this thing or substance that is their 'gender' aligns itself with 'gender' in the pathological sense outlined above.
(Notice in passing the similarity to religious myths about souls and suchlike. Some - though not all - such myths fall to the same analysis.)
This reification/hypostatization move is essential if we're to try to go along with the currently fashionable societal narrative. ('Born in the wrong body' gives the game away if nothing else.) It's essential if we are to make sense of 'transgender', in particular. But like most such reification/hypostatization, it doesn't - because it can't - supply meaning where there was none. People (lots on MN) who say they can make no sense of being born in the wrong body, or of 'feeling like a woman' although being born a boy aren't lacking in imagination or empathy - they're just plumb right; there is no sense to such notions.
OP's Jenny thinks she's a girl in a boy's body. She's not wrong to think that; it doesn't make sense. (It's not even false, some would say.) Of course that's not a reason to treat such a child unsympathetically or in any way badly. There's no justification for treating people so. But what's wrong (apart from the intellectual crime of treating nonsense as sense) with allowing the currently fashionable trans narrative to guide our behaviour wrt this child or others is the succour this latter narrative - and behaviour - gives to the societal pathology of mistreatment of women/girls.
That's what I (terfishly?) think. Probably a bit long. But it's complicated.