While our project grows, at some point we realized that we need to create new projects and reorganize our dataset. One case is that we need to isolate one dataset from others in
Nope, there's currently no move or rename operation in BigQuery. The best way to move your data is to copy it and delete the original.
Follow-up answer: Your batch request created the copy jobs, but you need to wait for them to complete and then observe the result. You can use the BigQuery web UI or run "bq ls -j" from the command line to see recent jobs.