D&D 5E - Barbarian/Druid wildshape synergy question

I have a pretty good idea, but I don't want to leap to assumptions because I could be wrong.

For a moon druid when wildshaped, it says class abilities carry over, but you cannot cast spells or concentrate (when raging). So does that mean if you had a barbarian/druid, you could

*spend bonus action to wild shape into a brown bear with an AC of 13 (compared to the bear's natural AC 11) due to the unarmored defense feature of the barbarian
* next turn spend a bonus action to rage while in bear form

My gut reaction is yes, not only RAW, but because it would support the theme of a raging barbarian in bear form as well.

Am I mistaken?

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