What size MOSFET do i need to drive about 6A 12V load? Will small TSOP6 package do the job without overheating?
No you can't.

The power dissipation is too much for the device in that package.
For worst case estimation you need to use graph 4. The Rdson at max junction temperature, that is also the value used for package current rating,
is 1.7 times the one at 25C. 
Including switchin losses you will be around 1.7 W

Please note the Rth J-A written on the datasheet is :


Too optimistic (a small package like that will have ~ 30 C/W 
just between junction and board)
it is referring to a board with 1 squared inch of thick copper layer to 
spread the heat. 


On top you need to consider the worst ambient temperature the devices can meet. What is the usage and where it will be located ?

I suggest to use a mosfet in DPAK with ~ 10 mOhm or less to handle the power dissipation.