I suspect we'll see Meghan jump into royal duties fairly quickly. The palace was very wise to let Kate have time to ease into the role, given that she had no experience dealing with the public beyond being swarmed by paparazzi. Meghan doesn't need as much hand-holding and quite likely doesn't want that, given the amount of experience she has giving speeches, being photographed by the press and going out on humanitarian visits for World Vision.
My gut says we'll have to wait a little bit to know for sure which causes she's going to make her own in this role, though. I'm guessing there will first be a phase of her tagging along to all of Harry's events, but even after she starts doing things solo the first order of business will be getting her to as many different corners of the nation as possible so that she can get to know it first hand. There are always ribbon cuttings, anniversaries, etc. that can help KP send her all over the realm. A specific charitable agenda will take a little more planning and discussion, especially if they want to craft a focus that ties into the other work being done by William, Kate and Harry's trust.