个子 = stature (height)

It is the Northern Chinese way of saying the built or body height of a person, a noun.

现在她很高了 would be fine and also natural; 现在她很高 also would sound like her height is changing spontaneously. It is difficult to explain, but I think mostly it is because Chinese is heavily based on the context. If you mention 了, I can understand it as a state now (that she is tall) as a result evolved from a previous state (that she was not used to be tall); Without 了, simply 她很高 already means she is tall at such moment, and mentioning 现在 additionally hints that she was not tall just a while ago. This will be alright if you say 现在她的血压很高/Her blood pressure is (very) high now, because blood pressure may fluctuate within a short time, and the sentence just point out an instantaneous observation now.

她现在个子很高 is natural.

Actually, 她现在变了很高 is not very natural. It would sound like she was shot by the magical enlargement gun. It is better to say 她现在变得很高, or even better, 她现在长得很高(了), 她现在长高了.

I think this is one of those things where it sounds right if you're from a specific part of China. I studied in the South, so I'm not sure, but this sounds Beijing-ish to me.

國語不是我的母語不過好像是大陸人比較習慣用個子.

In Taiwan 他現在很高了 is what people usually say. 大陸人常常用個子。 At least, that's what a native speaker told me.

I'm not native but I agree with you. It does sound a little strange

她！ “她的个子很高” sounds better， right？

Possible, but the emphasis shifts to "Now".