heatmap plots a heatmap of a rectangular matrix z, which is your
[1,1,1,1,1,1,1,1,1]
despite that this isn’t a rectengular matrix.
Try first
heatmap([1 1 1;1 1 1;1 1 1])
which results in your expectation.
Or to have it more visually appealing:
heatmap([1 2 3;3 2 1;2 3 1])
To provide x and y labels you use x and y vectors of strings
heatmap(["1","2","3"],["1","2","3"],[1 2 3;2 3 1;3 1 1])
See examples in the docs:
http://docs.juliaplots.org/latest/generated/plotly/#plotly-ref28-1