Where have you created the field? On the basis that you have created it at the Project level (as you said you wanted it on the property card. You would just create a workflow rule on the task level that every time a record is created or edited (and it evaluates to just tasks with a name of "Instrument Installation" it updates the parent project field you have created with the new date.
Run only when the following conditions are met
If True =
$Name = 'Instrument Installation'
Change: $ParentProject.InstallationDate (obviously you'll need to specify the correct field)$
If the task doesn't exist in a given project, the parent field will be blank, where it does exist it will be populated.
This will basically update the Installation Date field whenever any attribute of the task is updated (e.g. % complete, or updated due date etc.)
Keep in mind this will only trigger when the task is updated. If the tasks are already completed on existing projects, it won't fire, in which case you'll need to create a custom action to trigger setting the value as a baseline.