That is a nice looking part but I think your specs are too ambitious. .01mm is taxing for most big VMCs never mind an 85 lb benchtop mill. A 10 degree C shift in temperature will expand your material more than that.
That said, a Taig can certainly do a good job on a part like that though it will take a while to do that pocket. Using a .25 in cutter figure about 20-25 ipm at between .05 and .1 inches DOC.
Also your corners are square. That can't be done with a mill. You will have to radius your corners. Avoid too tight a radius since that will force you to use a very small end mill for a finishing pass. You would have a hard time finding a small diameter end mill that will cut that deep. This isn't Taig specific btw. A part with those square internal edges would normally be cast or forged.
Good luck and keep us posted on your progress.