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Over the next few days Harry could not help noticing that there was one person within number twelve, Grimmauld Place, who did not seem wholly overjoyed that he would be returning to Hogwarts. Sirius had put up a very good show of happiness on first hearing the news, wringing Harry's hand and beaming just like the rest of them. Soon, however, he was moodier and surlier than before, talking less to everybody, even Harry, and spending increasing amounts of time shut up in his mother's room with Buckbeak.

"Don't you go feeling guilty!" said Hermione sternly, after Harry had confided some of his feelings to her and Ron while they scrubbed out a mouldy cupboard on the third floor a few days later. "You belong at Hogwarts and Sirius knows it. Personally, I think he's being selfish."

_{Harry Potter and the Order of the Pheonix}

I think "Don't you go feeling guilty!" here is an imperative sentence. But I would expect an imperative sentence go something like: "Don't go feeling guilty, you!". The structure of "Don't you go feeling guilty!" is more like a rhetorical question. Is it a normal form of an imperative sentence? How should we understand it correctly in this context?

You are right to understand it as an imperative sentence that specifies, instead of implies, the subject. The formulation tends to come across as excited or dramatic because the unnecessary pronoun adds emphasis.

The structure that you expect ("Imperative, person addressed!") is typical if you're using a person's name or title, but is unusual when using the pronoun "you."

With the pronoun "you" the common form is "Don't you [do x]..."
Some frequent examples: "Don't you dare," "Don't you worry" and "Don't you cry."

Sometimes both the pronoun and a name/title can be included. "Don't you worry, mom! I already did all my homework!"

I think that @Katy has explained very well that it's an imperative. Let me quote a reference for completeness.

According to the Cambridge Dictionary:

Imperatives with subject pronouns.
For emphasis, we can use you in an
imperative clause:

[a student and a teacher]

A: Can I leave the room?

B: No. You stay here.

In negative imperatives of this type, you comes after don’t:

Maria, don’t you try to pay for this. I invited you for lunch and I
insist on paying.

Let's answer your questions

The structure of "Don't you go feeling guilty!" is more like a rhetorical question

It may share the structure of a question in relation with the order of the elements: auxiliary verb, subject and main verb; but it's not a question at all.

Is it a normal form of an imperative sentence?

Yes, it is.

How should we understand it correctly in this context?

Hermione is exhorting Harry not to feel guilty.

This is an older form of the imperative which has become a kind of fossilized pattern in that construction "Don't you go [verb]ing".

Compare from Shakespeare's King Lear:

Sit you down, father. Rest you.

or Two Gentlemen of Verona:

Here, take you this.

or from William Congreve's Love for Love (1695)

Hold, hold. Don't you go yet.

In conversation, depending on which word receives emphasis, the negative applies to the action or to you:

Don't you go doubting me now. (like the others who are doubting me)

Don't you go doubting me now. (don't become doubtful of me)

'Do not you go feeling guilty.'

Here, do is not a question. And go is a state of being, not a movement.

"Preform not you entering into a specified state of guilt."

go : 4. enter into a specified state

do 1. preform