You can actually use that website to look at your transits. When you go into the "Extended Chart Selection" it should automatically choose natal chart, with the Placidus House system. What you're going to want to do is click on a drop box to get to your natal chart with transits.
Then you'll need to put in a date you want to look at the transits for. The blue highlighted area is where you will do that:
I pulled up the Nov. 13th [2009] just to take a look at what was going on.
[deleted chart by request - Moderator]
You did indeed, have the transiting Mars square natal Pluto [within a 2-3 degree orb]. But I also noticed you had a couple other things going on. Transiting Mars was also square natal Mars. Also, transiting Mars is conjunct your moon...which of course squares the natal Mars and Pluto. Then you have some other transiting planets conjunct Pluto it would seem. Look up those aspects.
The Mars square Pluto transit is going to be a pain...especially since Mars is Retrograde for awhile too. With that Mars in your 4th house it wouldn't be surprising to be having issues with family/the domestic scene.
But to answer
exactly when the transit would have started would depend on what range of orb you are looking at. I believe squares are a 5 degree orb...so that would probably put it around the 10th of November.
I wish you luck in your research, but also with any problems you're dealing with *hugs*