FcgRIIIb rats and humans are not quite similar but in many positions sequence is the same (see Uniprot alignment: Uniprot 1.JPG), (https://www.uniprot.org/align/A20181231E5A08BB0B2D1C45B0C7BC3B55FD2655602380CP this link works only 7 days).
Affinity of rats IgG's for human CD16b probably will not be so strong like human IgG but looks it is possible.