Hello dinesh401,
you can do it, and it will function. The problem is only, that your output voltage is a little bit lower then 120V about the losses inside the transformers (DC-resistance of the windings and iron-losses). The smaller the power of the transformers, the greater the losses.
I do it like this, to make power supplies for little valve amplifiers. So I have a cheap isolation to the main input. Also I can take the filament voltage from the first transformer.
For your example you need 120V and 12VA. In this case I would take for the first transformer 120V / 12V 15VA or 20VA (12V 1,25A or 12V 1,6A) and for the second transformer a secondary voltage of 9V as input and power of 12VA. So you can minimize the losses.
Regards
Rainer