for any fish it's better to put them in a cycled tank I would imagine... the fry being so small they would be more vulnerable to the ammonia spikes as the new tank is cycled. Just dipping a filter sponge in tank water isn't going to add the right amount of bacteria to your water I wouldn't...
It's definitely Camallanus worms.... My mother's 55 gl is currently infested with them and she accidently spread it to my two tanks by borrowing my net. From what out LFS and internet research has told us they are extremely hard to get rid of, we live in Canada and we can't even get the worming...