Moving SQL Server Agent Job Categories and Schedules
Another cool powershell utility that I use everyday for server migrations is Start-SqlServerMigration.ps1 written by Chrissy LeMaire

It is very adaptive with different options.

Eg. In your scenario for migrating jobs with schedule, you can use 


  .PARAMETER MigrateJobServer
  
  Migrates all job server objects, including proxy accounts, job schedules, shared schedules, alert system, job categories, operator categories, alert categories, alerts, target server groups, target servers, operators, and jobs. Existing objects will not be deleted, and no -force option is available.


e.g. The PS below code will move all the databases (overwrite if the same name databases exists since it uses force parameter) from Source sqlserver\instance to Destination sqlcluster. It will exclude Northwind, pubs databases. It will migrate all the logins except nwuser, pubsuser, "corp\domain admins", will migrate all the sql agent jobs, will export the sp_configure options from source to destination server.

.\Start-SqlServerMigration.ps1 -Source sqlserver\instance -Destination sqlcluster -AllUserDBs -ExcludeDBs Northwind, pubs -IncludeSupportDBs -force -AllLogins -ExcludeLogins nwuser, pubsuser, "corp\domain admins"  -MigrateJobServer -ExportSPconfigure -UseSqlLoginSource -UseSqlLoginDestination