Is the sentence correct?

Well, I don't think I would use the word 'shuddering'.

This is how shuddering is generally used:

Though it sounded like a promising program to desperate restaurateurs, the program came to a shuddering halt on June 30 when funds were depleted, leaving a trail of distressed, confused, and angry restaurant owners unsure what’s next.

Since my brake job, they no long shudder when I use them.

I shudder to think of what she's going to do next.

Your sentence: It is shuddering to know that she would have no scruples to repeat all her actions and cause the same disaster again.

I would use words like: appalling, dismaying, alarming...

You could also say:

I shudder at the thought that she would have no scruples to repeat all her actions and cause the same disaster again.

Thanks, Mame, for your detailed reply.