Did great with this in a few games until I ran into Diana. Ugh. Too much range, burst, and defense (even without defensive items). Any ideas?

Diana is tanky because of her shield, and she deals large amount of aoe damage, and that's a problem for AD Malz. Since you rely on your voidlings to deal damage, anyone who can easily dispatch them (or even kill them without even trying) will be a huge problem, and you may want to swap out with someone else at that point.

I've ran into 2 AD Malz (well, one hybrid, one ad) playing as Morde, and I ate them alive. There was no way for them to ever have more than one voidling out, and they usually died before they even got their first morph.

So yeah, you can probably deal with her until you're about level 9-10, and then you'll probably need to swap with someone else. You'll have gained a fair amount of gold at that point, as well as a lot of mana in manamune so your time bot will not have been wasted.

If you're really stuck bot for the whole game (nobody wants to swap for instance), you should probably start playing very passively. Nuke the minions, stay on your side of the lane or even close to your tower, and leave it to that. Pushing the lane will most likely result in multiple deaths, so you might as well just keep the lane at a stalemate. If she dives you, combo her with your ult and hope you deal enough damage that she'll back off, and ping for help. Sucks, but sometimes there's not much you can do.

Don't forget that if you're in a really bad matchup, you can always swap to AP Malz. Being less dependent on your minions might work out better for some matchups, even if it means playing with the wrong runes / masteries.