It wouldn't be an issue for the Queen giving her permission, but it could very well be an issue if they want to marry at Westminster Abbey. But if they want St. George's, then things should run pretty smoothly.
As for the American issue other posters are talking about. I do think it's an issue. Not for HM or for the rest of the BRF, but for Meghan herself. This would be a giant culture shock for her. As a self-described "loud, brash American" and a feminist. She would have to accept a muzzle on her mouth and personality. She would go from a country where everyone is born equal, at least in theory
. To a country with an ingrained class system, she will curtsy, she will address some by their titles, she will have to put up with a tabloid media that sneers at her social mobility.
Then she will have to give up acting, a passion of hers. She will have to say goodbye to her role with the UN, as the BRF carefully avoids the UN. Camilla, Sophie and Catherine all live close to their friends and family, and thus have an important support network that they can see frequently. Meghan's friends and family live in North America, frequent phone calls don't fill that gap. She can't fly out to see them more than about twice a year, or the media will give her the "Air Miles Meg" treatment. She will be very isolated in a new world that is at odds with her personality.
Maybe they can make it work. But Meghan will have more emotional hurdles than any of the other current spouses. If their relationship continues, I hope Meghan gives herself plenty of time to consider all her options, and to test out if she can handle living in the UK - an ocean away from her other life. That's why I wouldn't want them to marry before 2019.
Given all the sacrifices she will have to make, this marriage would only work if she loves Harry 100%, 99% would probably end in divorce. So I guess the real question is does she love Harry more than she loves herself? Is she okay with his needs being put in front of hers? Is she okay surrendering her identity? It's a tall order, and I don't envy the position she finds herself in.