computed column making the select query to run slow
"Is this a good plan to copy the indexes." Indexes exist to improve the response time of read operations. Those operations arise from the workload. If the workload differs, the indexes should differ, too.

For example, it is not uncommon to have one server handle the OLTP activity and replicate the data to a second server where analytic queries are processed. The first server's work will be mostly single row lookups. The second's range scans and aggregates. In this case having different indexes on each server makes good sense. If all indexes were on both servers there would be additional, unnecessary work to do during writes and maintenance.