If I understand your question, you intend to copy the old drive to the new one. I'm not sure how you do this with a laptop, sounds interesting. Anyway, depending on what program you use to copy the old data to the new drive, you might be given an option to increase the size of the partition to 60GB. If not, you will wind up with a 30GB partition on the new drive, and 30GB of unallocated space. A program like Partition Magic will re-size and merge partitions, but there are no native Windows tools for such a job, so you want to get it right the first time. Suggest a thorough read of the manual/help files for whatever utility you are using to make the swap.
This is generally referred to as "cloning" a drive. But re-sizing the partition at the same time is a sort of a specialized job, and some utilities don't do it.