Your data is not enough. You need some data on the ground material (such as modulus of elasticity), body material and shape, etc. For example, if the ground is not hard, the force will be small.
EDIT (06/10/2013): As I said, you need more input data. I don't have time to give you a detailed analysis. You may wish to look at https://www.endevco.com/news/archivednews/2009/2009_02/tp321.pdf to get an idea about the essential factors of the problem.
The main thing that you need here is the notion of impulse. Consider Newton's second law:
$$\sum{\vec F} = m{\vec a}$$
In our case, the only relevant force is the contact force between our dog and the decoy. Before we move on, let's rephrase this force a little. Acceleration is the rate of change of velocity, and we know that momentum is given by ${\vec p} = m {\vec v}$, so we have:
$$\begin{align}
m{\vec a} &= m\frac{d{\vec v}}{dt}\\
&= \frac{d}{dt}\left(m{\vec v}\right)\\
&= \frac{d{\vec p}}{dt}
\end{align}$$
So, remembering from calculus that we can say, if $F = \frac{dp}{dt}$, then we can also say $F_{avg} = \frac{\Delta p}{\Delta t}$, we only need to know how much our dog changes velocity and how much time this takes. Let's assume our decoy stops the dog completely. Then, we have $v_{f} = p_{f} = 0$. Initially, we have our dog moving at $30 {\rm kmh} = 8.3 {\rm m/s}$, so we have $p_{i} = 250 {\,\,\rm kg\cdot m/s}$, so $\Delta p = -250{\,\,\rm kg\cdot m/s}$. Now, all you need to do is to estimate the amount of time it takes for your dog to come to a stop. I will contend that 10 seconds is too long, and 1 millisecond is too short. You can reason about this some more to come up with a range of estimates, but it's going to depend on the composition of your decoy and of your dog to get anything much more precise than an estimate.
Best Answer
There is no straightforward way to calculate the force of impact, because this latter is defined by the deceleration of the egg at the end of its journey as a function of time. In turn, this deceleration profile is defined by the elastic properties of both the egg and the surface it hits, and how each of these objects deforms and shatters during the impact. You can calculate the egg's velocity just before impact straightforwardly, but then the calculation becomes complicated by many elasticity and material properties which are probably almost impossible to measure. If you're really interested in the force of impact, it would most readily be measured, either:
Indirectly, with high speed motion photography of the collision so that you can infer the deceleration as a function of time; or
With stress sensors embedded in the impacted surface being sampled at very high speed, which directly measure the force on the impacted surface as a function of time.