DumboSunset is right that Asian Jewels has real private rooms, and the seafood tanks are the draw. I've done a 10-person birthday there; we had the back room to ourselves, and they didn't hover over the lazy Susan. One caveat: on a Saturday night the main dining room can be extremely loud, and the private room still shares a wall with it. If you go that route, call ahead and confirm the room has a door, not just the partition, and ask if there's a minimum spend (they sometimes won't quote one until you make the reservation).
For a more low-key option, Lake Pavilion on Main St has a bunch of semi-private round tables near the back. The food is Hong Kong-style seafood, very consistent, and they were fine with two vegetarians at our table—they'll do pea shoots, mixed fungus, and a tofu clay pot that isn't just an afterthought. We ordered the whole steamed flounder and the crab with rice noodles. They didn't rush us, but we also tipped well and told them upfront it was a birthday.
If you want stronger vegetarian entrees, ask for the Buddhist-style menu; they usually have one in Chinese but the server can tell you what's available. Another thing: with people coming in from Jersey, factor in the walk from the LIRR/Main St. Lake Pavilion is closer to the 7 than Asian Jewels, but both are fine in decent weather. With 10 people, I'd make the reservation for 6:30 or 7:00, not 8:00—the good round tables in Flushing tend to go to the early seating.