A compound sentence needs a comma, yadda yadda yadda…
She looked down at her blood-stained hands, and a small giggle rose up in her throat. “Who could’ve guessed?” she laughed. “Killing is so much fun!”
Do you want an explanation of why the first sentence is compound? In the first half, the subject is she, and the verb is looked; in the second half, the subject is giggle, and the verb is rose. Each part has its own subject and its own verb; you could write the sentence as two shorter sentences if you wanted to, just by deleting the conjunction and replacing the comma before it with a period: She looked down at her blood-stained hands. A small giggle rose up in her throat.
(WordPress’ spell check insists could’ve is not a real word; it says would’ve is the correct replacement. Mercenary Proofreader would like to know who the hell programs this thing to be so stupid.)