Do you have a male to fertilize the eggs? If so and you want to keep them, then yes, you need to move them. Make sure that the water is only a few inches high though! They will need to be abl to reach the top for air. If not, it would probably be smart to get them out of your tank. Your female will eat some of them and if she leaves any behind, there is a possibilitly that they will grow fungus and contaminate your fish. It is not a fact that your female has to be chased to lay eggs. If the female feels that the temperature is right, she will release them. My goldfish Denise was in a tank by herself last spring and still layed eggs. She did not have a partner until last fall. What I keep my fish in is regular spring water. You can get it from wal mart of food lion. I would move your eggs into a one gallon goldfish bowl until they are bigger and put them in a larger tank as they grow. That is what I do. Keep an eye on your fish and it would be great if you would keep in touch and let me know how she is doing.

My email is: armywf@hotmail.com or you can add me to your messenger if you have it at: snugglebug_04@hotmail.com. Good Luck With Your Fish!
P.S. I just joined this site but I have been raising gold fish since I was 8. You can count on my advice!