I think the out-of-plane definition is ambiguous as it is not clear which atom in the plane defines the apex of the out-of-plane bend.
In any case, I think what you want to do does not require any constraints at all. The optimizer in Q-Chem preserves point-group symmetry, so if you want to optimize a planar structure, just ensure all your atoms are in the plane to begin with. That way you will have at least Cs symmetry which will get preserved during the optimization.
It turns out setting up such an initial structure is not as easy as it should be in IQmol, so I have attached a C2v structure for you to start with. If you want to relax the additional symmetry so that you can obtain a lower Cs energy, simply lengthen one of the O-H bonds to break C2v symmetry.
$molecule
0 1
H 0.0000000 2.1490474 -2.0412432
C 0.0000000 1.2014162 -1.5120289
C 0.0000000 -0.0000000 -2.2272071
H 0.0000000 -0.0000000 -3.3120709
C 0.0000000 -1.2014162 -1.5120289
H 0.0000000 -2.1490474 -2.0412432
C -0.0000000 -1.1777540 -0.0983375
H -0.0000000 -2.1379714 0.4107496
C -0.0000000 0.0000000 0.6930995
O -0.0000000 0.0000000 3.3862223
C 0.0000000 1.1777540 -0.0983375
H 0.0000000 2.1379714 0.4107496
H -0.0000000 0.8242539 3.8899816
H -0.0000000 -0.8242539 3.8899816
H -0.0000000 0.0000000 1.7239328
$end