If you want to back up a website hosted at GoDaddy and upload it to your hosting account at Hostinger, follow these steps:
Log in to your GoDaddy account and obtain your IP address, FTP username and FTP password.
Connect to your GoDaddy FTP account using an FTP client. We recommend FileZilla.
Navigate to the location of your website's files, e.g. the public_html folder.
Select your website's files and directories and then drag them into the Local site section on the left side of the FileZilla window.
NOTE
Websites created with the proprietary GoDaddy website builder cannot be downloaded or migrated.
Additional Resources
Here's a full guide to migrating from GoDaddy to Hostinger: How to Delete a GoDaddy Account and Move to Another Hosting Platform
You can check the guides from GoDaddy here on how to download website files: Move a cPanel website with FTP and FileZilla and database: Export MySQL databases
If you need further help, make sure to contact GoDaddy support