I don't think you want to use the object type - that is a serialized php object.
If your different tasks are truly only slightly different in structure, you could use single table inheritance to keep all of your tasks in one table, and then use a self referencing one-to-one relationship to manage the dependency. Yes, the table would have extra null columns for different task types but your actual entities would be independent of one another.
There are some considerations for inheritance mapping strategies outlined here: http://docs.doctrine-project.org/en/latest/reference/inheritance-mapping.html#single-table-inheritance
The self referencing association is demonstrated in the Doctrine docs here: http://docs.doctrine-project.org/en/latest/reference/association-mapping.html#one-to-one-self-referencing