Hello, dear!
My best suggestion would to be to check out some tutorials online and see if any of those suit your needs. You would probably do well with the broomstick as a handle fine enough, and attach the axe itself after making the "blade" out of, I would suggest, foam mats. If you're looking for something cheap, those square puzzle-fitting foam playschool mats are sold all over the place, including Walmart, Target, and online! While the surface isn't smooth, you could use a gesso paint or many layers of mod podge to smooth it out.
Building props for the first time is a lot of trial and error, which is why I suggest looking up some videos on your search engine. I really enjoy watching Kamui Cosplay videos, [ url=
http://www.kamuicosplay.com/tutorials]which you can find here[/url], though I do not think she has a tutorial on foam matting.
For building from the mat, you will need...
one or two squares (depending on how thick it is--they come in different thicknesses some places)
some form of glue or epoxy (craft stores have full aisles of glues that will suit any need and material)
an x-acto blade and holder or a knife
pen/sharpie to draw the shape (I suggest doing it on a piece of cardboard or large paper first to get the shape/size you want)
gesso/mod podge/some thick glue paste to smooth out the surface
paint
sealant
patience
Make sure to watch those tutorials! I cannot help you more from here other than hopefully laying a ground for you to build off of! Good luck!
I'm going to take your advice on it, and also look at those tutorials. I'm naturally artistic so it shouldn't come out too bad. (hopefully) Thanks for the help.