Hi John Betong! Thanks for the welcome! Well, the reason the client didn't buy anything is because she doesn't understand anything of that, but she wanted her own hosting package, that's why she asked me to buy it. Unfortunately, I didn't think about this until after I bought the domain in GoDaddy. I made a research after this and found out I can transfer the domain, but didn't know about the hosting.
You're right Rubble, I'm sending a ticket to HostGator asking them as well, let's see what they say.