As long as the current isn't to much for the frogs and you have the room you could have both running at the same time. If you have any extra space in your current filter now you could also fill the empty space with extra sponge or other filter media. I won't take as long as if you were fishless cycling, I haven't had to do it but I would get it going as soon as you can. If you only take 1 of the 3 filter medias from a 10 gallon and add it to a 20 gallon it may end up going through a mini cycle. I think the easiest would be adding a second filter to the 10 gallon.