This design would be perfect for a 2-fabric applique, and it's easier than other forms because you aren't dealing with lots of small pieces that you have to position just-so. You can see examples of patterns for sale with this technique here -
http://prqc.com/2faq.htm - and examples of some that I made here -
http://www.quiltingboard.com/t-144873-1.htm
It would be very easy to make your own 2FAQ design since you already have the bulldog, and it's in 2 colors. You can use either needleturn or raw edge.