The plot is showing this behavior. Change the PlotRange to see it more clearly.

Plot[Q[\[Omega]], {\[Omega], 0, 3}, 
 PlotRange -> {{0, 0.05}, Automatic}, PlotStyle -> {Black}]

Better still is to check the limit of the function as [Omega] -> 0

In[6]:= Limit[Q[\[Omega]], \[Omega] -> 0]

Out[6]= 0

The plot is showing this behavior. Change the PlotRange to see it more clearly.

Plot[Q[ω], {ω, 0, 3}, 
 PlotRange -> {{0, 0.05}, Automatic}, PlotStyle -> {Black}]

Better still is to check the limit of the function as ω -> 0

In[6]:= Limit[Q[ω], ω -> 0]

Out[6]= 0