Since the question was "thoughts?" here are some:
Be advised, a DB Export via the Azure managment pages produces a BACPAC which is not transactionally consistent (see http://msdn.microsoft.com/en-us/library/hh335292.aspx).
A DB Copy as you expressed above (Create Database as copy of liveDB) is transactionally consistent, but when it is finished it is billable as it will have the same edition and database size as the source database (see http://msdn.microsoft.com/en-us/library/azure/ff951631.aspx).
As JuneT mentions, using an Automated Export is transactionally consistent, because it first creates a DB Copy, then does a DB Export. Because databases are billed in increments of a day no matter how long the copy is online, if you had a daily backup, you would be paying double the cost of your source database because of the copy coming online before the BACPAC is produced. Once the BACPAC is produced the copy is no longer needed by Automated Export, but you'll still be charged for a prorated day of use. Your retention settings will also impact billing as it relates to storage accounts since you'll be paying for stored BACPACs in terms of their size.
see http://blogs.msdn.com/b/sql-bi-sap-cloud-crm_all_in_one_place/archive/2013/07/24/sql-azure-automated-database-export.aspx
and
http://msdn.microsoft.com/library/azure/ee621788.aspx