Is it correct to write a noun after so + adjective like in this example " She has so beautiful eyes".
So can be used as a degree adverb to mean very, extremely, or to such a great degree. It's used in the pattern of so + adjective such as her eyes are so beautiful. It's incorrect to use eyes (noun) after so beautiful. Instead, you can use "such" in the pattern of such + adj + noun. For example, she has such beautiful eyes.
You can write so + ADJ, however the sentence above is not correct grammar because someone cannot have 'so beautiful' anything. Your sentence above should be:
"Her eyes are so beautiful."
You can write 'so' + ADJ to describe what something is.
[EDIT] Just felt that I needed to provide another example or two of when you can use 'so' + ADJ. Also, I forgot to mention in the original post -- Notice that 'so' is used before an adverb (adjective which describes a verb).
1) That car is so fast!
2) That car moves so quickly!
3) That car travelled so far!