Hi Kaeleb,
First, where is "here"? You don't mention where you live and it's not on your page so ...
Second, by "Australian Gum Tree" do you mean Eucalyptus? If so, which one specifically? There are over 500 species of eucalyptus, do you have a particular one in mind?
Third, why do you want to graft maple branches onto a "gum tree"?
Theoretically you can graft anything to anything but successful grafts are usually made onto related/similar stock. Citrus varieties are usually grafted onto citrus stock, stonefruits onto stonefruit, rose onto rose, etc. Maple and eucalyptus, not much in common there. And again, why?
You stated you are "extremely new to planting", welcome to the gardening community! Your interest and enthusiasm are to be commended so hold onto those but study up on your botany and horticulture basics a little bit more.
Good luck!