They are both OK, but "I'll pass your message on to her" is probably more common. Note: It should be "on to" not "onto." The "on" is actually part of the verb "pass on." You could write: "I'll pass on your message to her." "Onto" means to put something on top of something else. Example: He climbed onto the horse.

Thank you so much. Your explanation is just amazing and helpful. Today from you I learned that "onto" and "on to" can have a completely different meaning. I always thought they're just the thing :)