As yourworstnightmare, said...Which muslim country? It's basically a convenient label on several different entities.
Just for comparison, look at the diversity of European colonisations in America to have an idea how it would work for Arabo-Islamic colonisation.
That said, and in a realistic way (meaning we can rule whatever remains of Al-Andalus safely), the best candidate is Morroco if you manage to keep Castille and Portugal out of the coast, or during Saadi dynasty in the late XVIth century (especially under Ahmad al-Mansur)
- Plantation economy and slavery are going to exist as well. On this regard, Spanish kingdoms and western Arabo-Islamic entities were really close (giving that Castille inherited Arabo-Andalusian economy on this regard, that's hardly surprising).
- Giving the blunt racism on Black slaves, I doubt Morroceans would see natives any better than them. If something, without the necessity to ally with them, they could do as bad or even worse than Spaniards.
Forced conversion, native slavery (between associated use with black slaves, up to "Slaves coast" as in eastern Africa) are to be expected.
You'd have several differences though.
- Maintain of native entities when converted, rather than blunt conquest. Think of an equivalent of Morroco's policy on Western Africa
- Likely maintain of tribal politics on New World, a more divided socially and politically speaking.
- More maritime minded colonists than in Morocco (you always had a reluctance when it come to seafare in Morroco), maybe with the colony serving as regional "metropole" rather than a distinct rule from North Africa.