Vacuum press several thin layers over a former, you could substitute 1.5mm skin ply for the inner layers with 2mm MDF outer layers if you can get hold of it. I am assuming it is a "flat" door with no frame & panel detail.
I have seen a type of mdf being used by Handy Andy (she made me watch it yer 'onour) that has one side that has been grooved to allow it to bend and make curves. Seemed to work okay I seem to recall. Don't know where you'd get it from, although I guess you could make your own with a router and a straight edge.