Although Ginger is not toxic to dogs in small amounts, it's probably not a good idea to give her the actualy gingerale as the carbonation may make her tummy feel worse than it already does. If you wanted to water it down a little and give it to her without all the bubbles, that would be better. Also, you can find 'ginger' treats in the pet supply store designed specifivally for dogs that will help with nausea, so you may want to consider that as a possible solution to Clem's tipsy tummy.
I would withhold food for at least 12 hours to give her tummy time to settle, but provide plenty of water (or Pedialyte) to help prevent dehydration. If she's still not improving in 24 hours or so, I would give your vet a call.
Please let me know how Clem is doing and if I can help further.