Making the Mac more left hand friendly
Unfortunately, you can't change the location where Notification Center Alerts and Banners appear. This is a huge gripe of mine as well, and I highly encourage you to complain about this issue to Apple here:
http://www.apple.com/feedback/macosx.html
I'm not sure whether this is really a left vs right-handed thing.
All English speakers read left to right, so have a tendency to put our work left-aligned.
I am right handed, but work left-aligned, the same as you, so the distance to any Banner notification is about the same.
To give you more time to reach a Notification, you could either change Notification type to Alert rather than Banner, in Prefs > Notifications [needs setting for each Notification type]
or you could change the length of time Banners stay on screen - using Terminal.
defaults write com.apple.notificationcenterui bannerTime [time in seconds]
eg defaults write com.apple.notificationcenterui bannerTime 5 [which is what I think the default is]
You can return to clean defaults at any time by usingdefaults delete com.apple.notificationcenterui bannerTime
Each change requires that you relog.
Source: OS X Daily - Change How Long Notification Banners Persist for in OS X