She might throw it up later or have diarrhoea, depending on how much she's eaten, but it shouldn't do any real harm. I think I'd be trying not to let her eat it in future, but I know how difficult it is to stop them eating everything when they're determined.
Was it definitely seaweed? I don't know where you are but a few areas, mainly south coast and south west I think, had a problem a while ago with white or yellow lumps of palm oil being washed up on beaches. It's attractive to some dogs and can cause serious illness or death. I haven't heard of any instances in the last few weeks, but thought you should be aware, just to be on the safe side.
My older Cocker, William, had an upset stomach after eating a very dead crab at a beach many years ago. He'd already eaten some before I realised what he was doing and got the rotting remains off him