OP, the comments about trammel bars is correct, because you aren't going to be able to buy ready made templates - but I think in your case that you shouldn't use the trammel directly on the workpiece, because it can be difficult to start and stop a cutvexactlybwherevyou need to. Instead you should use the trammel to make up a template jig for use with the router and use that on the workpiece
And the thickness of the MDF.
Your router is a little underpowered to cut, shape material over 12mm especially if you are taking 5mm or more material off.
There is, however, some possible mitigations here: by setting out the curve with a pencil (using a template), then jig sawing or band sawing to within a milimetre or two of the line (removing most of the waste)
before affixing the router template and routing to the finished shape it is possible to get a lower powered router to make an acceptable cut.
A larger diameter cutter (e.g. 19mm 16mm or at least 12mm) is preferable to a smaller diameter cutter and will heat up less resulting in a reduced risk less of scorching whilst making the cut (attaching a vacuum to remove waste also helps in this respect)
With a 1/4in shank cutter the OP will need to cut slowly, because feeding to quickly and making heavy cuts can overload the cutter which can result in the shank of the cutter bending or even breaking in some cases. The thicker the cutter shank, the less likely this is to happen, so an 8mm shank is better than a 1/4in (6.35mm) one, whilst a 1/2in (12.7mm) would be better still. I believe the POF1200 only runs 8mm collets as a max
Also, by swapping to a spiral router cutter instead of a straight cutter the power required to make such a cut will be reduced by something like 20 to 30%.
1200 watts may not be a lot of power, but it was all that was available in even professional/industrial plunge routers in the 1970s until the "massive" 1600 watt models came along...
Above: Elu MOF31 industrial plunge router from about 1969. 1200 watts at 18,000rpm fixed speed. Probably not too different in size to the OPs tool