Canon 60D, Exposure question..

Just purchase 60D + 50/1.4 and have a little time to play around. Yesterday I found the camera have the same exposure value within built-in flash fired or not. That make image a little over exposure every I use built-in flash but image get blur too since the object moving (my kid) . I use Av mode and think that shutter speed should increase when I use flash, but the camera seem to retain shutter speed too. For example If I do not use flash and use f 2.0 in Av mode and camera decide shutter speed 1/30, dont you think shutter speed should increase to 1/60 or so while I use built-in flash?

Will this happen if I use external flash too? I want high shutter speed in low ISO and think flash should help while I found not
Or may be I miss something? I need your opinion please...