In conjunction with the preorder event, Electronic Arts released a statement this morning giving fans a better idea of when to expect to be able to get another opportunity to play the game. In what Electronic Arts calls Beta Test Weekends fans will get a chance to play the game starting in September.
As anticipation grows, BioWare also proudly announced today that Star Wars: The Old Republic will open "Beta Test Weekends" starting this September. These weekend play sessions will be open to selected players worldwide and create an opportunity for fans to get a sneak peek of the epic stories, worlds, quests, battles and characters in the game. Please visit http://www.StarWarsTheOldRepublic.com to register for game testing and to stay tuned throughout the summer for more details as they become available.

Dr. Ray Muzuka also comments in the article that they are targeting Holiday 2011 as the launch for The Old Republic.
"We are targeting Star Wars: The Old Republic to be one of the biggest launches of holiday 2011"

As we get closer to September, we will let you know when more information becomes available on the beta test weekends. Thanks to Wolf68 and chronium for the tip.