Correct, but there is no need to calculate the charge Q. Just recognize that the charge is equal in both capacitors. C=Q/V, Q1=Q2, C1∙V1=C2∙V2. The voltage law gives V1+V2=18.
So just solve these two equations for V1: C1∙V1=C2∙V2 & V1+V2=18
V2=(C1/C2)V1, (1+C1/C2)V1=18, V1=18/(1+4.7/3.3) = 7.425