There is an inbuilt report available for this information. Simply navigate to the desired project, select 'Summary'. Towards the bottom of the page will be a heading 'Reports'. This contains the 'User Workload Report'. Select this and enter the desired users profile.
For further information on this report please check out the following great guide: https://confluence.atlassian.com/display/JIRA/User+Workload+Report
To create a filter that replicates this behaviour you would need to query on the assignee field. You would also need to add the 'Remaining Estimate' column via 'Tools' >> 'Configure Columns'. This query could then be saved for reuse. You are also able to export this to Excel if required. Finally, you could add the gadget, 'Assigned to Me' on the dashboard and include the field 'Remaining Estimate' in the section 'Fields to display'.
Hope this helps :)
Are you using Tempo? I cannot see this mentioned earlier in your query which is why I had suggested 'Remaining Estimate'? The 'Planned Time' field is not a standard field in JIRA OnDemand.
The Tempo plug-in is a 3rd party supported plug-in but I searched further for you and found the following documentation which shows a Tempo gadget that reports on the planned time per user: https://tempoplugin.jira.com/wiki/display/TEMPO/Tempo+6.2+Release+Notes#Tempo6.2ReleaseNotes-TimePlanning
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