score:12
General answer: it will probably depend what you define as "the shape". Ultimately, once landfall was made on opposite coasts (1820-1840), and land was proven to be there, it was a matter of looking at all the places a ship had sailed through without hitting anything, concluding that the coastline must be further south than that, and drawing in a dotted line to taste.
As Antarctica is basically circular, this worked out pretty well - the inferred coastline was broadly similar to what was actually there.
As successive expeditions reached new stretches of the coastline, the estimates were refined and the known bits were drawn in, until by the late-1940s early-1950s the whole coastline was charted.
Map as of 1911, for example: (source; more examples). Note that this is basically correct in its outline save for the spurious "second peninsula" in the Weddell Sea (no idea why that got in there) and a certain ambiguity as to whether Graham Land connected to the mainland or not.
The more precise answer: according to a helpful article in Polar Record, 1844.
The first map to use the new place name was published in 1843, and the first map to show a complete outline of the continent, estimated from expedition reports, was produced in 1844.
Bulkeley, R. (2016). "Naming Antarctica". Polar Record, 52(1):2-15
The four maps displayed in that article are shown below. Note that the map above needs to be rotated ~140° counter-clockwise to match the orientation of these maps.
Upvote:6
A very interesting question, as it turns out.
The coast of Antarctica wasn't definitively sighted until about 1820, so no globe until then would have featured it.
I found this pocket globe made by Abel Klinger in I believe 18801 that shows the barest outline of some of the coast of Antarctica. Examining some globes from the same manufacturer in 1855, I can't see any hint of it. One would imagine there must be one earlier than 1880 though2.
1- The text just says "end of the 19th Century". However, I've found other references to his pocket globes dated 1880. So I could be a few years wrong here.
2 - Vastly complicating this search is the fact that people don't like to show pictures of largely blank areas of a globe.