Animal agriculture is responsible for 18 percent of greenhouse gas emissions, more than all transportation combined.
Yes. In fact, some sources calculate that the FAO figure is actually an underestimate.
A frequently cited study on the topic is Steinfeld et al. (2006). This is the FAO study already mention in the question. It has 1503 citations on Google Scholar, although only 40 in the more conservative Scopus. I am not sure if it is peer-reviewed.
To judge its quality, we could look at what other scientific studies have to say about it. To pick one, here it is summarised by Koneswaran et al. (2008):
Although much evidence has been amassed on the negative impacts of animal agricultural production on environmental integrity, community sustainability, public health, and animal welfare, the global impacts of this sector have remained largely underestimated and underappreciated. In a recent review of the relevant data, Steinfeld et al. (2006) calculated the sector’s contributions to global greenhouse gas (GHG) emissions and determined them to be so significant that—measured in carbon dioxide equivalent—the emissions from the animal agricultural sector surpass those of the transportation sector.
The FAO report is also cited by the IPCC AR WG3 report.
A more recent study by Goodland and Anhang (not peer reviewed, but cited by at least 19 Scopus-indexed studies) claims that the FAO study actually underestimates livestock's contribution:
A widely cited 2006 report by the United Nations Food and Agriculture Organization, Livestock's Long Shadow, estimates that 18 percent of annual worldwide GHG emissions are attributable to cattle, buffalo, sheep, goats, camels, pigs, and poultry. But recent analysis by Goodland and Anhang finds that livestock and their byproducts actually account for at least 32.6 billion tons of carbon dioxide per year, or 51 percent of annual worldwide GHG emissions.
See also this article in The Independent which discusses the Goodland and Anhang paper. A further study is by Garnett (2011) (emphasis mine):
While there are no studies that quantify GHG emissions arising from the entire global food chain, there have been estimates of GHGs attributable to global agricultural production. The IPCC estimates agriculture’s direct impacts to stand at about 10–12% of global emissions (5100–6100 MTCO2 eq); this excludes emissions resulting from fuel use, fertiliser production and agriculturally induced land use change (Smith et al., 2007).
The figure rises to up to 30% when additional emissions from fuel use, fertiliser production and agriculturally induced land use change are included; land use change alone accounts for 6–17% (Bellarby et al., 2008).
One regional analysis for Europe finds that food accounts for 31% of the EU-25’s total GHG impacts, with a further 9% arising from the hotel and restaurants sector (European Commission, 2006). At the national level, developed country studies find food consumption contributes between 15% and 28% to overall national emissions (Garnett, 2008, Defra, 2009, Audsley et al., 2010, Swedish Environment Protection Agency, 2010, Regional Activity Centre for Cleaner Production, 2008, Nieberg, 2009, Kim and Neff, 2009 and Consuming Australia, 2007). Fig. 2 shows the breakdown of emissions at each stage in the supply chain for the UK food system. One UK study (Audsley et al., 2010) additionally quantifies emissions associated with food consumption-induced land use change and finds that this increases the food chain’s overall GHG contribution by 66%.
However, the Garnett paper considers both animal and non-animal agriculture, so these figures cannot be directly compared. However, they go on to state:
Since livestock utilise around 80% of the world’s agricultural land (FAO, 2009) and generate the bulk of the sector’s GHGs, there is a perception that efforts to raise livestock yields can generate both environmental and commercial benefits.
In summary: exact methodologies differ and it can be difficult to compare figures, a literature survey did not show significant disagreement with the FAO study. Do trucks with animals count to animal agriculture? Do trucks with meat do?
Studies that I found that disagreed rather considered that the FAO underestimated animal agriculture-induced emissions, than that they overestimated it. So: Yes, animal agriculture is responsible for more greenhouse gas emissions than transportation.
Steinfeld H, Gerber P, Wassenaar T, Castel V, Rosales M, de Haan C. Livestock’s Long Shadow: Environmental Issues and Options. Rome: Food and Agriculture Organization of the United Nations; 2006.
Koneswaran, G., & Nierenberg, D. (2008). Global Farm Animal Production and Global Warming: Impacting and Mitigating Climate Change. Environmental Health Perspectives, 116(5), 578–582. doi:10.1289/ehp.11034
Robert Goodland and Jeff Anhang. Livestock and Climate Change, World Watch Magazine, November/December, Volume 22, No. 6. Online PDF
Tera Garnett. Where are the best opportunities for reducing greenhouse gas emissions in the food system (including the food chain)? In: Food Policy, Volume 36, Supplement 1, January 2011, Pages S23–S32, doi:10.1016/j.foodpol.2010.10.010
P.S. Note that when people say emissions, they often mean net emissions, i.e. total sources minus total sinks. As the two are constantly in flux, total emission as such is not very meaningful (and quite hard to determine).