You may not be able to use Laplace transforms, the equations appear to be coupled non linear. If you will be controlling the the copter, you will be needing some form of a PID controller. Have you read the following article?

http://andrew.gibiansky.com/downloads/pdf/Quadcopter%20Dynamics,%20Simulation,%20and%20Control.pdf

It breaks down the physics and how to implement a controller. The only thing I didn't like about it was the ODE solver that was used. Forward Euler may work but I would use at least a second order solver (Modified Euler), or the "Classical" Runge Kutta Method. The micro controller that will be used for the copter will dictate what type of internal solver can be used.

Not my area of expertize here, and probably not answering your question directly, but Raffaello D'Andrea gave an impressive talk on the subject at TED:

http://www.ted.com/talks/raffaello_d_andrea_the_astounding_athletic_power_of_quadcopters?language=en

and certainly knows how to model these machines:

https://scholar.google.com/citations?user=FdGOel8AAAAJ

I hope it's of any help.

if you are interested in rigid-body modelling you have to model at least 2 different problems:

1)dynamics: from angular momentum conservation, model the body as 5 rigid body, the "fuselage" and the 4 rotors (remember they are rotating bodies), forced by rotor thrust. This results in only 3 dofs (pitch roll yaw) if you consider that rotors angular velocity is achieved instantaneously in response to a command. Otherwise you have additional 4 dofs and 4 equations.

2)aerodynamics: you can easily relate thrust and torque of each rotor with your control variable and state variables through stationary aerodynamics

This is obviously a very simple model, missing many phenomena.

I am trying to model only 3DOF at the moment.

Newton Euler method utilizes 6DOF at one time.

Any suggestions regarding this?

Consider just the 3 equations for angular momentum, but remember that total angular momentum is the sum of contribution from fuselage and spinning rotors. You can find the explanation of the problem in par 4.6 of: Etki and Reid, dynamics of flight-stability and control, third edition.

You can start by studying 3-DoF models of mounted quadcopter systems. They limit the translational motions and exhibit only rotational motions. You can start by this paper: 

http://link.springer.com/chapter/10.1007%2F978-1-84628-974-3_2

Also, there is a commercially well-known model available here: 

http://www.quanser.com/products/3dof_hover

This model is studied in the following link: 

http://personal.mecheng.adelaide.edu.au/benjamin.cazzolato/Quanser/Automatic_Control_II_Hover_V7.pdf

https://www.youtube.com/watch?v=Fi5GxqxinP0