Minimum pumping length of regular language
Your example in fact demonstrates that the pumping length can be smaller than the number of states in the minimal DFA. In your case the minimal DFA contains 3 states, but the pumping length is 2.

The pumping length of a language $L$ is the minimal $p$ such that every word $w \in L$ of length at least $p$ can be written as $w = xyz$, where $|xy| \leq p$, $y \neq \epsilon$, and $xy^iz \in L$ for all $i \geq 0$. 

If $L$ contains no words of length $p$ that's not problematic at all. For example, the pumping length of $\{ w \}$ is $|w|+1$. In that case the pumping property holds vacuously.