You can change all of those things except your grid. Here is the canned message for moving QTH:
When your move involves changes to state, grid or zone, you need to create a new, attached account for the new QTH. The reason for this is QTH information is taken from the user profile, so changing your existing profile would effect all the previous eQSLs you have sent.
First change the Callsign/QTH End Date of your current account to the date you moved. You do that from the 'My Profile' screen,
http://www.eqsl.cc/qslcard/editProfile.cfm.Then go to the 'My Accounts' screen,
http://www.eqsl.cc/qslcard/MyAccounts.cfm, and follow the instructions at the bottom of the page. Set the new QTH to start after the end date set previously.
If you have uploaded QSOs past the date that you moved you may need assistance with this, in which case please reply back.
73, Dave - VA3KAB