Unexpected results from scikit learn regression decision tree
This is the visualization for the inducted tree from your data:



As you can see, it can never predict [[1.5, 1.5]]. Your data is just too pure, the inducted tree will fit it perfectly, having all leaf nodes with only one sample. If a leaf node has more than one sample in it, then the predicted value is the mean of the y values for those samples.

Furthermore, trees are not the best model to induct the identity function ($y = f(x) = x$). Trees work by creating rules and dividing the feature space orthogonally (i.e. only vertical or horizontal lines in the feature space).

In other words, your model didn't learn that f(1.5, 1.5) = (1.5, 1.5) because a) there's not enough data, b) trees are not good at doing that anyway.