Electron beams from laser-plasma wakefield accelerators have low transverse emittance, comparable to those from conventional radio frequency accelerators, which highlights their potential for applications, many of which will require the use of quadrupole magnets for optimal electron beam transport. We report on characterizing electron bunches where double bunches are observed under certain conditions. In particular, we present pepper-pot measurements of the transverse emittance of 120-200 MeV laser wakefield electron bunches after propagation through a triplet of permanent quadrupole magnets. It is shown that the normalized emittance at source can be as low as 1 π mm mrad (resolution limited), growing by about five times after propagation through the quadrupoles due to beam energy spread. The inherent energy-dependence of the magnets also enables detection of double electron bunches that could otherwise remain unresolved, providing insight into the self-injection of multiple bunches. The combination of quadrupoles and pepper-pot, in addition, acts as a diagnostic for the alignment of the magnetic triplet.