Can you see the Milky Way as it shoots out from either side of The Southern Cross?
Just out to the right, about one cross span, is a bright spot.
Then about the same again is another.
That is eta Carina.
But if you can't see the Milky Way you will have trouble finding it.
Most of us dont even bother looking when the Moon is this full.
In two weeks time, it will be easy to spot.
Be patient, and in the meantime, look at it in stellarium.