A Q-Q plot is a great way to determine whether residuals from regression analysis are normally distributed.
here can see that (sometimes):
the normality test is statistically significant, indicating the data don’t follow the normal distribution. However, the QQ plot shows that they do. The sample size is 5000, giving the test the power to detect trivial departures from the normal distribution.
..., you’d conclude that your data are normally distributed. This is a rare case where statisticians will trust graphical results more than the hypothesis test!
concerning your Q-Q plot taking into consideration this table of distributions' Q-Q plots you can conclude that you're having bimodal distribution. But better make conclusion from the domain knowledge of your data: right-skewed data have positive skew (Mean > Median> Mode) - your plot can be described as Light-tailed truncnorm as well. I think, increasing sample size for sufficient statistics you could be able to get enough p-value not to reject H0: "The sample data follow the hypothesized distribution", where you test Poisson distribution. Because as I already mentioned in comments for count-data Poisson (or Negative Binomial for overdispersed Poisson) distributions are used