You can definitely use MOOSE to do this type of simulation. However, we don't have much capability to do alloy solidification built-in as part of the phase-field module as this point. So you will will need to be comfortable writing some code of your own to add capabilities. We do have some capabilities for pure material dendritic solidfication, you can take a look at the example
moose/modules/phase_field/examples/anisotropic_interfaces/snow.i
There is some capability for alloy solidification being worked on now but it will be several months at least before it becomes publicly available.