Alex, this sounds like a wonderful project, and could basically be done as you suggest.
The first concern is the long-term stability of your fill to raise the height. If you are located at higher elevations which receive much snow/rain, this is even more of a concern. In part, this depends on how much fill height is being used, but it sounds like you are planning on 12" or more. With that in mind, you'll want to choose your patio base fill material carefully.
For the base I would not use "dirt," but maybe a coarse chat or road base, compacting with a power vibrating tamper every 4 to 6" as the base rose from the existing ground level. This will provide a stable base which is far less likely to have settling problems in the future. Finish the base off with a 2 to 3" layer of coarse sand, also compacted, to set your stone on, then grouting your joints in sand or a #2 medium quartzite grit (also called "turkey litter"; makes a beautiful loose grouting for stone) A sloping soil fill can then surround the patio to accomodate plantings.