Good suggestions from Don in Holland and a good pic too. I used an ironwood mallet (via references in Eric Sloane's books) of branch and stem.It was strong & tough but it wasn't heavy enough. All ironwood I've kept for use seems to get punky and rot in 7 - 10 yrs.
I love basswood aka linden, for the nectar-loaded blossoms for the honeybees, as well as for the carveable,light, soft wood. Good for making lightweight boxes, not good for mallets
I'll look up elder for Don's elder root. We've got elderberries here. Alder maybe?
I'll go along w sugar maple, with a good curly grain. American elm is a top choice - really fibrous twisty grain, so difficult to split. I made 2 that have been in use for 30 yrs. One has a chunk split off one face. Think what are toughest woods to split, what don't you like to see as fat ones to have to split for the stove?
A curly pc of Amer cherry could be good too.
I think cherry will "ring" when dry & hard, more than elm, which is more "dead" and will absorb shock better.

Those leather-faced iron mallets w wood handles by Garland of Saco, Maine are hard to beat - good weight and balance and shock absorbing. Leathers are replaceable if you ever wear them out or if you leave one where your puppy can get it and chew it to mush.

Shine on!