For a “standard” linearly indexed array it is Int, which on a 64-bit Julia equals Int64 and on a 32-bit Julia equals Int32. Generally you can use any subtype of Integer for doing the indexing.
typeof(first(eachindex(v))) should work for your purpose.
Notice that this may be something other than Int, e.g. for
v = view(rand(10, 10), 1:2, 1:2) or v = BigInt(1):BigInt(2).