Oh, in that case it might help, but I don't think it will be as critical as in chess.
No I'm working on the nine men morris game for now. I will use quiescence search to return just the moves that will form mills. I think that would be similar to to capture moves in chess.
That's a very tricky thing to test. I would implement iterative deepening right away. You should then observe the behavior where after searching up to depth D, repeating the search gets you to depth D almost instantly. If that doesn't happen, you are probably doing something wrong.
Also, how can I test transposition tables to check that the code I added with regards to TT works fine?
You should pick a few positions and measure the number of nodes and the time it takes for the search to reach a particular depth. Although the speed in nodes per second will probably go down after implementing the transposition table, the time to reach a depth should go down.
Finally, you should play a match between your program with and without transposition tables. How many games to play is a tricky question, but I wouldn't do less than a thousand. They can be quite fast (for chess I use about 0.2 seconds per move). The important thing here is accumulating statistics. I would also observe the two programs playing at slower pace (say 10 seconds per move), so you can see what they are doing and notice if there's something broken.
I do what I described in the previous paragraph for almost every change to my program. If you don't do something like that, I don't think you can make meaningful progress.