It's neither neccessary nor preferred.
Your example is tricky as was (and other question words, too!) can both introduce an object clause and a relative clause:
Ich sehe, was du nicht siehst.
This was du nicht siehst is clearly an object clause. It is used as the accusative object of sehen.
Ich sehe was, was du nicht siehst.
Here, the first was is the accusative object to sehen, and the following clause is merily an explanation to the was. It's a relative clause.
Your example works the same:
Ich habe vergessen, was ich googeln wollte.
Here, was ich googlen wollte is an object clause.
Ich habe das vergessen, was ich googeln wollte.
Here, was ich googlen wollte is a relative clause referring to the demonstrative pronoun das. In sloppy speech, one may use es instead of das and make it a very weak accusative object. The meaning is the same.