For the you sheet where you don't want to copy over the zeroes, what you can do is insert a column and number each row you are copying 1 through whatever. Then sort the whole thing by the column with the 0's in it and that will place all the rows with the 0s at the top or bottom.
Then copy everything except the zeroes to the new sheet. Then sort the copied stuff by that column you numbered 1 through whatever and that will return it to its original order without any of the zeroes.