Hi cike
depending on the extent of your redesign - it should be definitely possible to re-arrange some of the form elements via CSS. Potentially - as you say - you could also do this with Javascript however this is generally not recommended (i.e. extracting and re-injecting elements in a different position via Javascript) as it can lead to a clunky user experience.
As an alternative, the form definition can be changed in terms of Layout however this kind of customization is currently not available in Studio and can only be done via an engagement with Lithium Professional Services.
What I suggest is to get in touch with your Account Manager so that your designs can be reviewed to determine the best course of action (potentially even using a mixture of the above approaches)
Hope this helps,