For countries that depend on resources, as opposed to manufacturing and services, does not low population equal more profit per person? In the general sense that is.
Only if the profit is distributed equitably. In resource-extraction economies, the power over the resources (armies to keep them safe, capital to extract them, power to give exploration contracts to foreign companies) tends to fall into the hands of small circles of owners who then use their wealth to run patronage networks and capture the state. A particularly egregious OTL example would be Equatorial Guinea, which on paper has a big GDP per capita due to big oil income and small population. However, the authoritarian family-state running the country not only controls the production of income (the president's nephew runs the state oil company, his son is the vice president, and so on) but the income itself. Consequently, Equatorial Guinea has spent its income on building vanity cities in the jungle or spend/save it overseas while large parts of the population remains deprived of basic services. Meanwhile, the small population (and consequent small workforce) constrains economic diversification through manufacturing/agriculture.
While
@Ricardolindo did bring up some positive counterexamples, even Gabon
has been run as a family-state, which recently beat back a coup attempt that could (nothing's confirmed yet) signal underlying unrest.
I therefore don't think Niger can become a high-HDI (life expectancy, education, GNI per capita) country off uranium alone. Herding offers more promise-- the assets required for herding (cattle, goats) don't require massive companies or state structures to maintain. They can be owned by families and sold to other families. As the Sahelian belt becomes more economically interconnected, pastoralism offers a way for common people to advance themselves, and build up the resources needed to enter other modes of living. In South Sudan, the cattle trade with Uganda remains strong, and some refugees have used the proceeds to complete their education in Ugandan colleges. (
Unfortunately, some seem to have been caught up in "degree farms".)
However, even pastoralism ultimately runs into a wall of sorts. Nigeria is currently affected by a spate of conflicts between herders and farmers over scarce lands in the center of the country. As the population grows, herders may find themselves in similar land wars with farmers or with each other. Those who stand and fight may link up with regional crime syndicates or terrorist groups for an advantage. Those who leave for greener pastures may do so for the same reasons-- Ali Darassa, leader of a rebel group in the Central African Republic, is a Fulani from Niger. His UPC rebel group contains large contingents of Fulani, who are either first-generation migrants to the CAR or the descendants of historical migrants.
Ultimately, I think to fulfill the AHC, pastoralism would need to grow but also phase itself out after some time. After initial expansion that enables the population to advance above subsistence level, it would have to consolidate through a phase of enclosure and ranching. At this point, some might leave the lifestyle-- selling their land plots to developers and investing in urban transport/trade. The developmental model here may be less China and more Missouri/Nebraska: solid economic base in livestock, with secondary functions in regional transport and shipments (along the Niger river, or through rail hubs in Niamey, Matadi, and beyond). These secondary functions may then be extended into a services industry of some kind (Niger's northern mountains were an adventurous-tourist spot until the 1990s Tuareg rebellion, I think). Other models for this kind of development may be Alberta in Canada. I would cite Argentina's beef empire, but the Rio de la Plata gives the Argies an edge that landlocked Niger can't exactly match.
Frankly, the idea that I have imagine recently, was a sort of Taureg-Kanem empire formed as an analog to the Kushan Empire. Namely, a semi-nomadic and semi-sedentary empire focused upon the trading routes and dominating nearby migrant peoples while simultaneously gathering large amounts of gold tributes from nearby states, such as Mali, preferably Muslim states in the north and states to the east such as Makuria and the Abyssinian lands.
Though it doesn't fit OP's request, it's an interesting possibility. As it stands, Niger is divided into 3 rough zones: a Zarma/Songhai west around Niamey, a Hausa/Fulani southeast around Matadi and Zinder, and a Tuareg north around Agadez. Tying these all together under a precolonial state framework is technically feasible-- the Sultanate of Damagaram in Zinder had a Kanuri ruling class, a Hausa populace, and was quite comparatively rich from trans-Sahel trade income. Nana Asma'u of the Sokoto Caliphate was fluent in Tuareg, in her station as scholar and diplomat. However, it seems these Kanuri states (and especially Kanem-Bornu itself) had troubles with dynastic legitimacy and military weakness. The last iteration of a Bornu state-- Rabih az-Zubayr's domain-- was a parasitic warlord realm which lived on the income from captured war slaves sold to Egypt.
Maybe Tuareg intervention could introduce a loyal army around which a more lasting state structure could be built? Instead of being identified with remote mountain complexes in the desert, Tuareg
kels (clan confederations) could be based in villages and cities (like the Qizilbash Turkic confederacies of Iran) and become involved in the politics of surrounding kingdoms (like the Afshar and Qajar subsets of the Qizilbash, which later became imperial dynasties). Either way, they'd have to deal with the many of the same problems OTL's Fulani states did, with impending French/British competition over the Sahel being the most challenging.