The genetic architecture of behavioural traits in dogs is of great interest to owners, breeders and professionals involved in animal welfare, as well as to scientists studying the genetics of animal (including human) behaviour. The genetic component of dog behaviour is supported by between-breed differences and some evidence of within-breed variation. However, it is a challenge to gather sufficiently large datasets to dissect the genetic basis of complex traits such as behaviour, which are both time-consuming and logistically difficult to measure, and known to be influenced by non-genetic factors. In this study, we exploited the knowledge that owners have of their dogs to generate a large dataset of personality traits in Labrador Retrievers. While accounting for key environmental factors, we demonstrate that genetic variance can be detected for dog personality traits assessed using questionnaire data. We identified substantial genetic variance for several traits, including fetching tendency and fear of loud noises, while other traits revealed negligibly small heritabilities. Genetic correlations were also estimated between traits, however, due to fairly large standard errors, only a handful of trait pairs yielded statistically significant estimates. Genomic analyses indicated that these traits are mainly polygenic, such that individual genomic regions have small effects, and suggested chromosomal associations for six of the traits. The polygenic nature of these traits is consistent with previous behavioural genetics studies in other species, for example in mouse, and confirms that large datasets are required to quantify the genetic variance and to identify the individual genes that influence behavioural traits.