I have the setup of Solr cloud running in my local machine with the internal Zookeeper (i.e) Zookeeper that is being internally used by Solr with the single node.
My query is that while I move my Solr to the production environment, Is it recommended to run the Zookeeper in a isolated/separate/external instance or is it better to go with the internal instance of Zookeeper that comes along with the Solr?
The use solr internal zookeeper is discouraged for the production environments. This is even stated in SolrCloud documentation.
Although Solr comes bundled with Apache ZooKeeper, you should consider yourself discouraged from using this internal ZooKeeper in production, because shutting down a redundant Solr instance will also shut down its ZooKeeper server, which might not be quite so redundant. Because a ZooKeeper ensemble must have a quorum of more than half its servers running at any given time, this can be a problem.
The solution to this problem is to set up an external ZooKeeper ensemble. You should create this ensemble on a different machine so that if any of the solr machine goes down it will not impact the zookeeper and rest of the solr instances. I know currently you are going with one solr instance.