If you need the supply to give 1-1.2A then you need a transformer >1A. At the very least 1.5A, preferably more.
Don’t forget that a transformer will O/P AC, so you will need a bridge rectifier and smoothing caps.
The 7805 is rated at 1A so is not suitable if you need >1A. Also not advisable to run anything at, or close to its maximum rating.
If you were to draw 1A from the 7805, with a 7v drop across it (12v - 5v), you will be dissapating 7W, so you will need a fair sized heatsink, as well.
A better option would be to get a PSU with an O/P of at least 9v @ 2A, and then drop the voltage with a buck regulator module. There are plenty available on eBay.
Even better would be to get a plugpack (wallwart for those who live across the pond), with a 5v, >=2A O/P.