If your backups are scheduled as SQLServer Agent Jobs, they can be scripted out and then run against your new database.
I don't think you can script the maintenance plans, but a little-known fact is that they aren't anything more than glorified Wizards that create the SQLServer Agent Jobs. After this, they serve only to define what databases the job should apply to.
See Books Online for the xp_sqlmaint procedure for more details. This is the procedure that the jobs use, and you can use it yourself without going through the maintenance plan wizard.