There's one way, but it might be disappointing: use an additional variable (or one of the table's field) for storing the count, and increase it every time you make an insertion.
count = 0
tbl = {}
tbl["test"] = 47
count = count + 1
tbl[1] = 48
count = count + 1
print(count) -- prints "2"
There's no other way, the # operator will only work on array-like tables with consecutive keys.