The production, directed by Phillip Breen, will also star Desmond Barrit as Falstaff.
Dobson was most recently seen onstage playing Joan Crawford in Bette and Joan on tour, that followed a run at London's Arts Theatre. Other stage credits include an Olivier Award-nominated performance in Bryony Lavery's Frozen at the National Theatre, and appearances in the West End musical Budgie and as Gertrude in Hamlet on tour and in the West End, opposite Ed Stoppard.
To book tickets, contact the box office on 0844 800 1110 or visit www.rsc.org.uk for more details.