Jocelyn asked her mom, "What was it like when you were a child?"
No, your sentence is not punctuated correctly. When reporting direct speech, you should use quotation marks to enclose the spoken words. Additionally, you should use a comma before the closing quotation mark to separate the spoken words from the reporting clause. Here's the correct punctuation:
"One day I'm going to be an astronaut," Adelle told her sister.