By nature, linear transfer functions are only valid for small signal and a defined bias point (Vgs/Vds/Id). To derive a transfer function, you need to specify the bias point. Then you shouldn't have problems to determine the linear MOSFET parameters. You're apparently assuming a voltage source driving the FET, thus Cgs won't affect the transfer characteristic. Cds and Cgd should be considered together with the load impedance, however.
If the objective of your analysis is large signal behaviour, simply forget about Laplace and transfer functions. You need to proceed to non-linear differential equations instead.