I don't know whether there are taxis waiting at Amtrak, nor whether they are from reputable operators.
But if your cell phone works on the train, you could call Mears Taxi at 407-422-2222 when you're about 30 minutes from the station, and request one to meet you there. Mears operates under 3 brands: Checker (the WDW concessionaire), City, and Yellow. They will also have the Mears name on the rear end.