Here are some (prospective) tour dates for the start of the World Tour! I don't consider them official until they are posted on AvrilLavigne.com, but they are most likely real. Source.
2011.5.16 at Marine Messe in Fukuoka
2011.5.17 at Osaka Jo Hall in Osaka
2011.5.21 at Saitama Super Arena in Saitama (near Tokyo)
2011.5.22 at Saitama Super Arena in Saitama (near Tokyo)
2011.5.24 at Nihon Gaishi Hall in Nagoya