Hi @volak. Thanks for being part of GoDaddy Community! Whether or not your website will go down in the process of moving to a VPS depends on a number of factors. In general, if you set up the server and get your website files copied over to it and properly configured, you should be able to change your domain's DNS to point to the new hosting and avoid any downtime. If you need specific help, I'd recommend getting in touch with our customer care team. They can review your situation and give you more specific recommendations. Others may also have suggestions here if you provide more information on your particular situation.
JesseW - GoDaddy | Community Manager | 24/7 support available at x.co/247support | Remember to choose a solution and give kudos.