Move your filter pad over to the new tank with the goldfish. You're the one that has the Eclipse 5 gallon, right? If so, the Biowheel in your Eclipse should have enough bacteria to deal with what bioload you have left in there after the goldie is out, so you should be fine to take out the filter pad. Just use it as an opportunity to replace the pad, since as messy as goldies are you're probably due for a switch anyway.
When you move the goldie over, just float the old filter pad in the new tank for a few days. This will likely not instantly cycle your tank, but should only take a few days as opposed to weeks in a normal fishy cycle. Even so, keep your test kit handy and be prepared for ammonia and/or nitrite spikes, which should subside quickly with a couple of pwc
The 10 gallon would definitely benefit the goldie, but do you think you could bump it up to a 20 gallon instead? They don't cost too much more and your fish would be healthier and happier as a result. The filter I would recommend for a 10 gallon would be the Aquaclear 50 (200 gph
). Normally I'd shoot for 10x turnover but I guess for a goldfish the extra turnover wouldn't hurt. If you can score a 20 gallon I'd go with the Aquaclear 50 or 70 (300 gph
), or the Emperor 280. JMO.