See the person next to you? Kill! Kill!!! KILLL!!!!
I'm your baby! Can you feel it?
The Doppelgänger only copies the value, not the character itself, so it would be discarded.
The Witches ability refers specifically to the Witch being immune, not to characters of a certain value.
Hope this helps.
A bit late to the party, but I'm afraid Pedro's answer is not correct.
The Doppelganger initially has no value at all. He searches for (and copies) a value from the card below him, after the effects of Wizard and Witch have been resolved.
So in Sven's example, this is what would happen:
1. The Wizard would cause the Queen to get discarded.
2. The Witch would (only) cause the Wizard to get discarded (since the Doppelganger is a card with no value at all at this point and thus is not affected by the Witch).
3. The Doppelganger would now copy the value of the Witch and be worth 1.
=> As a result, the owner of the Doppelganger would now be awarded the goal card, as the score for the column is now tied at 1, but of course the position of the Doppelganger is closer to the goal card than the Witch.