Copy cell data from one w/sheet to another with unused cells left blank

Hi - i've got a workbook with two sheets. Sheet1 has a list of place names in column A and dates in column B. I want the same list to be entered onto Sheet2 in the same order. I can use the formula: ='Sheet1'!A1 and essentially it works just fine except in cells where no data exists on Sheet1.
If I drag that formula down to empty cells on Sheet2 I end up with a 0 in column A where no data exists in the corresponding cell on Sheet1. The date column on Sheet2 has 00-Jan in the cells where no date exists in the corresponding cell on Sheet1.
What I'm after is for the blank cells on Sheet1 to also be blank on Sheet2 until data is entered into Sheet1. it just makes it all look cleaner and more professional.

thanks,