Druid/Barbarian- wild shape +unarmoured defense

When in wild shape, you use the stats and the default AC of the creature.  If you take levels in Barbarian to get the Con bonus to AC, would that be added?

Yes, but possibly not in the way that you're thinking, just going by the way you worded that.

The Barbarian's Unarmored Defense feature doesn't provide a "Con bonus to AC". It gives you a different way to calculate your base AC when you're not wearing armor: 10 plus your Dexterity modifier plus your Constitution modifier.

Because this is a class feature, and Wild Shape lets you retain your class features, you can still use this method of calculating your base AC if you want while you're in Wild Shape. Because your Dexterity and Constitution are replaced with those of the beast form, you'd use those modifiers instead of yours. So in this situation you can either use the AC given in the stat block, or 10 + the beast's Dexterity modifier + the beast's Constitution modifier. (Obviously in practice you're going to pick whichever of those is higher.) What you can't do is just add your Constitution modifier to the beast form's base AC, because that's not what Unarmored Defense does.

So, say you are transformed into a Brown Bear, which has an AC of 11 according to its stat block. The stat block's Dexterity modifier is +1, and its Constitution modifier is +2, so Unarmored Defense would give you an AC of 13 in that form. There are other forms, like Dire Wolf, where it wouldn't make any difference, and potentially some where the Unarmored Defense AC would be worse than the stat block's base AC.

It's also worth noting that in 5.5e, Circle of the Moon Druids have their own special AC calculation to use while in Wild Shape, which is 13 + their Wisdom modifier. 

Thanks for the clarification! Makes more sense this way.

Also, if the Moon Druid had magic armour ,  would that be added to the AC, or would it also be overridden by the 13+WIS? 

Quote from ZebulonIndex >>

Thanks for the clarification! Makes more sense this way.

 

Also, if the Moon Druid had magic armour ,  would that be added to the AC, or would it also be overridden by the 13+WIS? 

The Wild Shape feature has this to say about using gear while in beast form:

Worn equipment functions as normal, but the DM decides whether it’s practical for the new form to wear a piece of equipment based on the creature’s size and shape. Your equipment doesn’t change size or shape to match the new form, and any equipment that the new form can’t wear must either fall to the ground or merge with the form. Equipment that merges with the form has no effect while you’re in that form.

So it's up to the DM whether the Druid's armor can be used at all while in Wild Shape. If the DM rules that it can, then it would be an alternative base AC calculation to the one provided by the beast form stat block. You would choose which of the two to use.