yeah, you definitely want to get the right kind, i've seen it called Mother of Thyme, Creeping Mother of Thyme or Coccineus Thyme but i would not buy any until i saw it flowering to make sure it is the right color. there's a lot of variations out there and the names don't seem to be used consistently. i know for sure that i do not know the specific name of this we have planted here because it was a long time ago and the tags are long long gone.
if you were closer you could come get some chunks of it. i've never harvested seeds from this so i don't even know what the seeds look like or when they're ready. i could go look and see if any are out there (tomorrow since it is dark now)...
it also does require a fair amount of sunshine - i'm not sure you have that where you are at?