Augustine was wrong about many things. This is one.
The Augustinian notion was to riddle everything with the angst and guilt that he felt over his past sins. Thus, he could envision a God who would put an infant who had not actually committed any sin into a corner of hell, and to have them endure a "light punishment."
Rather, it is much more realistic to envision God as the Hound of Heaven, as in the Francis Thompson poem, who pursues every soul and gives that soul every option to choose Him. That would include infants, albeit in a way about which we can only speculate.
But we should always speculate in God's favor, since He's shown us that He will always work to save us.
Augustine was wrong about very little. This was one of them--that unbaptized infants go to hell. He was corrected on this matter by Anselm and Innocent III etc. But it's one of the few things he was wrong about. Blaming him for angst and guilt is typical Enlightenment nonsense, reading Augustine through Calvin's and Jansenius's eyes and repudiating Calvin and Jansenius rather than Augustine. Augustine is made to be the whipping boy for a lot of the modern folks' own stupidities. No theologian offers a greater emphasis on the healing that grace brings to the guilt-ridden soul than Augustine--though many equal him none surpasses him. If you are not aware of that, you don't know Augustine's theology very well. You know caricatures of it, which are a dime-a-dozen.