There are many options to migrate records (items or document) together with metadata (colums).
If possible in your case, the best is to save the original library as a template choosing the appropriate option to save also the content, then create the new library that will maintain all previous columns, metadata and also content type (if used).
If you have already created the new library and you cannot start from scratch, 1st you have to ensure that the destination library has the same columns (or you create the same), than you open both libraries using explore view and you copu (or cut) and paste: alternatively you can use move option for each document (more heavy job if you have many items)
If these 2 options are not feasible in your case, then think at powershell scripts and/or workflows, but keeping in mind that original copied documents will maintain their metadata, but these will be not visible in destination library if the destination library will not have the same columns
Hope this help to clarify the basics