First - I note that you ask ...
Can I setup the backup w/o loosing my data on my original drive?
I want to make it very, very clear - RAID1 is not a backup - and even with a RAID1 array you will still need to back up your data.
To deal with your questions - the DNS-323 will work fine without having identical drives, you can use any brand or model of drive
provided it's capacity is the same as, or larger than the first drive - this is very important, it is possible for one drive to be described as a 1TB drive and have a capacity of perhaps 983GB (I'm just pulling figures out of the air here) whilst a second drive also described as 1TB might have a capacity of 979GB - if the drive you started out with was the 983GB one, you could not create a RAID array using the 979GB one - BUT - if things were the other way around, there would be no problem.
If you were using a 1TB drive as the original and a 1.5TB drive as the new one, you would obviously not run into the problem I just described.
Depending on the firmware version in use - I believe this was introduced in either 1.05 or 1.06 - when you install the second drive, the format screen will have a check box that you can check to have it create a RAID1 array, what should happen is that the system will create a 1TB partition and format it and then sync the two drives to give you a 1TB RAID1 Volume_1.
It should also configure the remaining space as Volume_2 - however I have not personally tested this - I have created RAID1 arrays with drives of unequal sizes and know that this is what happens if the array is created with both drives in the system, and I have also tested adding a second drive to the unit and creating a RAID1 array with drives of the same size and I know that that works also.
Now - what I also know from experience - is that if you have a RAID1 array with a JBOD Volume_2 as described above, and a drive fails, when you replace that drive, and the unit successfully recreates & resyncs the RAID1 array, the JBOD Volume_2 is lost, so - I would not be very surprised to discover that creating a RAID1 array "on the fly" with a larger disk does not result in the expected two volumes - if I find the time, I'll test this and see what happens.