And where is the Manchester "Baby" SSEM? The IAS used Kilburn-Williams tubes for memory, and the SSEM was the testbed that proved that technology. Hence the IAS could not have been built before the SSEM.
In the 1946-1949 time-frame, there were lots of people working on the stored-program paradigm, all cross-fertilising each other. Which machine was actually first became more luck than anything else, but the big problem they had to solve was memory. A large memory was essential, since a small memory could hold intermediate data, but not the program. Mercury delay lines and the Kilburn-Williams tubes were the technologies that made the stored-program computer possible. After 1948 when those became available, the stored-program machines followed thick and fast: EDSAC in 1949, LEO in 1951 and so on.
By the time the IAS was operational, not only had the SSEM been working for four years, it had been replaced by the Manchester Mark I and that had been upgraded to the Ferranti Mark I; the world's first commercial computer. The first of those was delivered to the university the year before the IAS became operational.
Von Neumann's position as the inventor of the Von-Neumann model is safe, but whether it is his baby or not, and whether it is the purest expression of his ideas or not, the IAS seems to hold no great place in the history of computing. Rather that place seems to be taken by EDVAC by way of Von Neumann's report on its design in 1945, a year before work began on the IAS. EDVAC itself did not run before 1951, still a year ahead of the IAS.
The time-line doesn't mention the Commodore Pet either, and that was also a seminal moment in computing. The Altair made no impact on industry, whereas the Pet did; it was the first office micro-computer.