Why are views not copied over when using SQL Server Log Shipping?
All modifications to the source database will be copied over to the target database, assuming that your log shipping process is not broken or blocked.  The target database must be in read-only made (which in your case it is) but users accessing the database will prevent SQL from applying the transaction log.

Log shipping needs to be able to put the target database into single-user mode before applying the logfile.  This is the one serious drawback of log-shipping.  Try disconnecting all users, then wait for log shipping to get caught up.  Your view will appear.