You can read the talk from which this quote is taken here.
If you don’t want to read the whole thing, scroll down to “To those who leave,” and read the context surrounding that quote.
Too often, when we are members of a belief system that is targeted by those who hate (and yes, Catholics, I’m talking to you, here, too…you know all the anti-Catholic clap trap out there), we are tempted to go to the wrong folks when we have questions. Rather than going to our own leaders and our own sources to find the answers, we find ourselves being taken in by those whose first and only goal, in talking to us, is to destroy us. You know these people: Jack Chick and his clones…even such surprising folks as Andrew Cuomo and Jaimie Stiehm, a writer for US News and World Report.
These folks are not out to help you resolve your doubts; their entire purpose is to expand them and make you doubt more. YOU know what your doubts and questions are; you better than anybody. Only if they simply cannot be answered by your own should you go elsewhere…and that’s what is meant by 'doubt your doubts before you doubt your faith."
Never leave your faith because someone is playing to your doubts. Leave only if someone else has so profound a truth to offer you that you leave with gratitude to your present belief for the way it prepared you to accept further truth from God.
So yes, Elder Uchtdorf is right. doubt your doubts before you doubt your faith.