The round, square, or rectangular portable cast iron forges with a cast rotary blower are extremely hard to document before the 1890's or 1900's, and then usually with the Pump Handle. The hand-cranked blower pushes the general time frame into the 1910's and 20's. Just look in the Farm section of a reproduction Sears or Wards catalog from the early 1900's. Right there you will see pictured the same portable forges that soo many people drag around to Living History events. They are fine for general small work, but are very out of place at anything from the Civil War on back.
Yes, hand cranked mechanisms existed before then, as did rotary blowers and portable forges. But the shapes/styles/look of them was very different from those 1900's cast iron portable forges.
During the Civil War, the Army on both sides had forge Wagons that traveled with the army. When they would settle in somewhere for a while, they would build up a forge out of stone and mud, and then attach their bellows to it. In the 1870's and 80's, the cavalry had a pack forge - a square metal box that everything packed into. But it was a unique and specific pattern. They continued in use up through WWI and even part of WWII.
The bellows is the COMMON air supply that is easiest to document for the 1700's on up even into the early 1900's. Before the 1700's, you have to start transitioning from the great bellows (two stage) back to using two single-stage bellows.
The actual forge is up for interpretation. The only documented portable "forge" is the forge cart or waggon. The forge and bellows are all built into/onto a cart or waggon. These varied in size from a small tinkerer's cart (like a large wheelbarrow) on up to the back of a full sized waggon. The traveling blacksmiths who didn't have that forge-cart or forge waggon, would build their forge on site out of rocks and mud.
There are some great drawings of forge carts and tinkerer's carts in the drawings of W H Pyne in the book Rustic Vignettes For Artists And Craftsmen isbn 0-486-23547-5. Pyne's drawings are from around 1815, and primarily in England.
I hope this helps. Of course, these are but my humble opinions, and best used in conjunction with your own research.
yhs
Mike Ameling