I have some problems on uploading the DB on new server...i'm trying to upload with PHPmyAdmin but when i'm try to upload this (it's over 1GB). There is another way to import a DB without PHPMYAdmin?
As @Brogan has suggested, use SSH. Copy the file to the server, login to MySQL with the relevant user, and select the database you want to import it into. The use the source command and point to the sql file to import.
You could move the DB dump.sql file to a non public directory your new server using ftp but you would still need to SSH in so you can use the command to import it into mysql.
I'd get in touch with admingeekz. They migrated my 14M post board with indeed 0 downtime. They live sync the new server somehow, then simply change DNS over.