If you want to put the goldfish in the tank then buy a test kit so you can test the water.
API Master test kit is the best.  It will test ammonia/nitrites/nitogen and ph.  That way by having the test kit you will be able to see ammonia levels when they rise and be able to perform water changes accordingly.
The only other think I would recommend is bacteria booster such as API's stresszyme.  ADD IT RIGHT TO YOUR FILTER!  This will jump start the cycling process and will help your tank to cycle faster. Add more once a week.

Also, no matter how cute they are  and how much your daughter begs PLEASE do not buy any more goldfish for about a month or so until this tank is cycled.  Ammonia and nitrites should read zero and Ph you want around 7.2-8.0 (alkaline) nitrates no higher than 40 mg/l. Then it is safe to add another fish!

Also, I use a water condtioner by aqueon and it keeps ammonia and nitrites at a minimum.  I love it!  And you can use it with the API stresszyme!  I've never had tanks cycle so quickly before!  Good Luck and keep us posted and ask any questions if you think of any.  Someone will answer and try to help!
POST PIX!  WE love PIX!!

ONE OTHER THING!
Sorry, I forgot to add that please while the tank is cycling and the goldfish is the tank, please only feed him once a day or once every other day!  And only as much as he can eat in a minute!!  Just until the tank cycles. Then you can feed him a bit more twice a day.  Overfeeding while a tank isn't cycled is one of the biggest reasons for fish to die.  It put's too much wastes in the water too quickly!  Your fish wil produce wastes just by breathing!  
Have fun with your new friend and may he have a long and happy life!

I agree with what everyone else has said and I would put him into the tank as long as the ammonia etc. doesn't read to high. To make it cycle quicker I was thinking you could add a bit of water from the bowl into the tank, it might help that little bit
Best of luck.

Glad you got a 20 gallon

I have only one thing to add aside from what has already been told, and that is, that no matter how much your daughter wants new goldfish, get her at most one more! 10 gallons per fish is the absolute minimum!

the only other thing is do u have a fancy gold fish (fantail) or do u have a comet or common fish. both of the last 2 will get up to a foot long so if u do get a second fish and we all know u should and will. get a fantail they stay smaller

And they might get bullied by the commons/comets. Which will sooner or later kill the poor fantail :C