Putting aside the question of whether 99% accuracy is sufficient
OK, I'll ignore this.
I find it hard to believe that children can pose for three hand gestures
The law linked by OP defines "age-restricted user" as "an Australian child who has not reached 16 years." It's fine if age-restricted users cannot pose: they will be rejected as ineligible. I'll consider accessibility concerns as out-of scope and won't address them in this answer.
technology can accurately determine if they are over a certain age or not.
Has this been shown to be technically possible?
I consider this to be OP's main question, so that's what I'll answer below.
Is this prone to deceptions?
OP didn't ask this question. Even so, I'll briefly discuss it. However, this is more of a pragmatic/security issue than a skeptics.SE question.
Does this research exist?
The claim makes reference to a "recent innovation", so I'll guess that they're referencing some paper along the lines of the 2024 paper, Predicting human chronological age via AI analysis of dorsal hand versus facial images: A study in a cohort of Indian females.
I'm treating this particular paper as a representative paper, as it's the first one I found. It's admittedly not the best choice: It uses a dataset with participants aged 20-80 years whereas the proposed law is intended to provide a younger separator.
The research behind the paper was to use a computer to process images within a hand and face data sets. Hence, there are likely to be numerous similar papers produced in a similar manner.
How could a hand photo be used to estimate age?
Quoting that paper:
As people age, the skin loses elasticity and becomes thinner, which can cause wrinkles and creases to become more prominent. Moreover, it can cause the veins and tendons on the dorsal side of the hand to become more prominent, and the bones in the hand to become more visible, including zones of the knuckles, phalanges and metacarpal bones.
I'll take it for granted that the machine learning code trained by the authors found this or similar visible indicators of age.
What if the hand belongs to someone who is very close in age to the age limit
The machine learning system described above (and any similar system) will have estimation errors. E.g., the authors note a mean error of 4.7 years (presumably the error range is proportional to age, so this isn't necessarily as bad as it sounds). Due to such error, such a system is not very reliable in filtering out those who are close to the legal line. The submission authors acknowledge this concern:
Where estimation is used, there is a need to provide alternative methods to correct false negatives, for example when a 14 year-old has been estimated to look under 13 so is initially denied access to social media (assuming 13 is the applicable minimum age).
...
But for the vast majority of people who are by definition more than +/- 2 years of any given minimum age, age estimation is a quick, convenient, privacy-preserving and effective method of age assurance.
Is deception a concern?
This is somewhat separate from OP's question. Even so, I'll reply to Paul Johnson's comment that such a system might be vulnerable to deception: The technique discussed in the paper uses gestures as a means to expose physical characteristics to a camera. I don't think this is necessarily any more prone to deception than using facial photographs and telling the subject to face in a particular direction (which are also prone to various forms of deception).
Nonetheless, barring some way to prevent it, deception is incredibly easy: The primary motivation for using hands rather than faces (which are, per the paper above, more reliable) is for privacy. However, that privacy also makes it easier to cheat by just using someone else's hands. Further, people are probably more willing assist in cheating such a system if it doesn't require them to leave behind a picture of their face as evidence.
Summary/Conclusion
The submission proposes to use hand pictures as an age estimation tool, specifically for those who are far enough outside the age requirement that such photos are reliable. That is, those who multiple years older than the legal age requirement can use such photos as a means of estimating their age, thus bypassing other, more onerous (and less privacy-preserving) methods of age verification. The paper I found strongly suggests that hand photographs could be used for this purpose (ignoring the deception concerns raised by Paul Johnson).
