Utilization of MOSFETs as switches, design methodology
Powermosfets like this are not meant to be used in their constant-current region (I call it that because people like to confuse saturation/linear, because they are flipped with BJT. In this case it would be saturation). 

When you do, they very often suffer from thermal runaway. As a result, you are pretty much always going to be in the linear region (which you will definitely be doing with the 5V gate-source you show in the schematic). The Rds(on) value is the only one you really care about. 

You can actually look at the figures in the Datasheet to see where you would be operating. In Fig.1 you can see that in order to get in saturation with a gate-source voltage of 5 V, you would need a drain-source current of 3 A. With your 9 V battery that would mean you have a maximum 3 Ohm total load. 

You can use the same graphs to figure out the Rdson. With a gate-source of 5 V, you can see that we have about 200 mV drain-source voltage for 1A drain-source current, or about 200 mOhm. Of course this gets worse with higher temperature, see Fig.4 for that.

As to what you should model the device with: Depends on what you are doign. If it is a simple DC circuit hand-calculation, the Rds(on) will suffice probably.