Yes, compared to wealthier countries in Northern Europe and North America, Peru appears poor, but a comparison to very poor countries with low-growth rates, like Moldova, Ukraine, Ghana or even Albania is bit unfair. Considering current rates of GDP per head, the potential for future growth, the prospects that membership of the Pacific Alliance brings, which joins Peru's economy to the fastest growing economies in the region, recent economic stability, the outlook for the future looks reasonably good for Peru. Bloomberg expects it to be one of the ten fastest growing economies in the world this year, just ahead of Thailand and just behind Malaysia. This goes back to the OP's original question and the problems of terminology and lumping all non-G20 countries into categories such as emerging economies, or Third World. These terms don't really give a full picture of what is happening in each country.
In Peru, there is still potential for bumps in the road in the next few years, with low commodity prices, lower government revenue, the recent sluggishness in the economy and the problems in a very fractured Congress, with the President and his wife distracted by scandal, but looking at the bigger picture, the outlook for tourism and the diversification of the economy away from commodities, which membership of the Pacific alliance brings, could help maintain high growth rates. While low prices for its commodity exports are a temporary problem and its abundance of natural and cultural resources if properly managed could still yield lots of wealth. While I think that rural poverty in the Andes and improving education should be at the top of any Peruvian government's to do list, my main worry would be the environmental damage that illegal gold and silver mining in the jungle causes (not to mention the environmental and social damage wrought by cocaine production) and corruption in the provinces, but greater transparency and international involvement could hopefully help mitigate these problems. And there are already many precedents for how things can continue to get better. Even in the last ten years, there has been many improvements, but compared to the dark days of the 1980s and Alan Garcia's first presidency, Peru has come a long way - Shining path exploding bombs in Miraflores, inflation reaching 7,649% in 1990, or a cumulative total of 2,200,200% inflation of the Inti over Garcia's five-year term.
Peru has its problems like any country, perhaps worse than many Western countries, but compared to somewhere like Ukraine (about to go bankrupt and in the middle of a civil war), Moldova, the poorest country in Europe (riven by a separatist movement in Transnistria which has declared independence) and Albania, which is regarded by Transparency International as the most corrupt country in Europe, suffers from high unemployment and much of its income is from remittances from workers who have left to work overseas, things don't look too bad for Peru.
Perhaps it would be fairer to compare Peru to someone like its neighbour Colombia, or in Asia, it is expected to have similar growth rates to Malaysia (richer than Peru, but with similar growth prospects) and Thailand (which it is closer to in terms of GDP per head, poverty levels, growth prospects and demographics). In Europe, the best comparison would probably be Montenegro, which has similar levels of wealth per person. But of course, every country has problems unique to its situation and any comparison invites criticism.
GDP per person (PPP) in 2014
Bosnia Herzogovinia $9,536
Ghana $3,992http://www.bloomberg.com/news/articles/ ... -this-yearhttps://en.wikipedia.org/wiki/List_of_c ... per_capitahttps://en.wikipedia.org/wiki/Transnistriahttp://www.bbc.com/news/world-europe-17679574http://www.bbc.com/news/world-latin-america-19928905
Nominal GDP per head paints a slightly different picture, but is still worth a look.https://en.wikipedia.org/wiki/List_of_c ... per_capita