As Guy says, the cut depth on the 201 is 0.75 inches, that is, the flutes stop at 0.75 inches from the cutting tip. The overall length is 2.5 inches so it should be possible to leave an inch and bit sticking out of the collet reasonably comfortably.
Did you mean that the router collet was rubbing the wood or that the top of the cutter was rubbing and burning?
Was your cut taking a series of steps down to the full 0.9 inches?
If you’re cutting an outline of 0.9 inches depth you may run into trouble with the cutter not being able to pull the chips out if you’re cutting a slot, this happens because the flutes need to clear the surface to eject the chips properly. In this case the main choices are to cut a slot wider than the bit to allow chip clearance (and suck out the chips with a vacuum or extractor) or to use a bit with longer flutes.
Here’s a couple of examples of cutters with longer flutes which can go deeper (but you have to be careful using long cutters, it’s easy to break them).