With Intel Matrix Storage manager, you can create a RAID1 mirror from two drives online, using one (old) drive as a source and the new one as target. It will sync in the background for several hours, making your disk access slower during that time, and that's about it. No need to reformat, repartition, etc.
You can use any disk, provided its size is equal or larger than the original disk, and the new disk is connected to the same SATA controller on your motherboard. Manufacturer of a disk does not matter. Moreover, it is often suggested to buy a different model disk, so if there is a systematic problem with certain disk model (like it was with Seagate disks not too long ago), at least one of the disks in your RAID would not be affected.
Sometimes same-capacity different model disks (e.g. 1TB) differ in their actual size by a few sectors. I've never had problem creating RAID1 mirrors from, say, 1TB WD and Seagate disks (with Intel Matrix Storage).
One other potential problem is the sector size. Some newer disks use 4KB sector size, while older disks all use 512 bytes sector size. I don't know how Intel Matrix storage would cope with different-sector-size disks, and what performance implications might be, but I suppose it's better to stick to same-sector-size disks. Check your disk, it is most probably has 512bytes sectors.