Let’s finally find out what Dickinsonia is.
My first thought was the Woolly Rhino. I could RULE the neighborhood! But then I thought wait, the other members of my home owners association would have Woolly Rhinos, too, and they might not take too kindly to me doing that. But then I thought wait, a Woolly Rhino War would be AWESOME!
In actuality, though, I like my neighbors. I think I’d pick the Dodo bird and invite them over for a barbeque. Historical accounts say they are quite tasty.
Variola Major is only extinct in the wild. So there!
That was a mommoth, not an elephant. Owners would have to deal with the shedding - I’m marketing my Malteses as hypoallergenic!
Mine’re smaller and the jury’s still out on the hair situation anyway.
Besides, if they are hairy, I can always shave 'em or aim the marketing round braiding them and putting little bows in.
Micro-mammoth© The ultimate pet for wannabe hairdressers!
“Micro” is a funny adjective for a pet that’s larger than a mastiff.
Wasn’t there a book and/or movie The Mommoth Prophecies? 
A giant lepidopteran with tusks is rumored to haunt a remote area.
In a follow-on, OP says: “It’s all linked up to an exceptionally well organised database of current common and scientific names, so you can pretty well try any name, and mostly it can work out what you mean, showing multiple images if multiple species share a common name or the spelling’s ambiguous.”
Seems like you could game this a little by typing in “tyranossarus steggorex” and having the machine show you a couple pictures of T Rex and Stegosaurus and asking “which do you mean?” So you could settle the feathers-and-if-so-what-color debate, and many others, without actually implementing the machine.
I’ve always wanted to see a live Dodo. I think it’s because it was the first species that I had heard described as extinct. I knew dinosaurs weren’t around any more, but it was specifically Dodos that I thought of when extinction came up. Probably because of the expression “Dead as a Dodo.”
And dodos probably taste good.
Some people said they were great, other said 'disgusting".
Probably depended on what they ate.
Also probably depended on how long the eater’d been living on mouldy ship’s biscuits.
Dodo. Do try and keep up 
More weevils than mold. “Remember to always choose the lesser of two weevils!”
I think dodos ate fruit and other vegetation, though. And the rest of the pigeon family is tasty. So they probably tasted pretty good.
You’re welcome:)
I ditto the Dodo. They deserve another chance.
Anomalocaris
Because weird
*Most people are familiar with the sad story of the dodo. This plump, flightless bird was so tasty and so tame that it was hunted to extinction within a century by Dutch sailors arriving on the shores of Mauritius.
Rather fewer people realise that this story is largely incorrect.
Tasty? Apparently not – the waste pits from the early Mauritian settlements, which were excavated for a study published in 2013, are full of animal bones from the Dutch dinner table, but there is not a single dodo bone amongst themHunted to extinction? Unlikely – Mauritius was blanketed in thick impenetrable rainforest, and dodos deep in the heartland would have been well beyond the reach of even committed hunters.
Plump? No – the tubby bird depicted in modern reconstructions is based on illustrations probably drawn from overfed captive birds or poorly-stuffed dead specimens. In the wild the dodo was a much leaner bird…But the sailors themselves did not make much of a contribution to the dodo’s extinction, says Claessens. “At most there were a few hundred people living in a coastal settlement,” he says.
The problem was more likely the ship rats and other animals they brought with them, which spread across the island, eating dodo eggs and outcompeting the birds for food.*
*But initial investigation indicates that dodos were eaten mainly because of their ease in capture and availability, not for taste; indeed, their alternate Dutch name was “walghvogel”, used in the journal of Vice Admiral Wybrand van Warwijck, who visited Mauritius during the Second Dutch Expedition to Indonesia in 1598. He explained the meaning of the name as follows: “… finding in this place great quantity of foules twice as bigge as swans, which they call Walghstocks or Wallowbirdes being very good meat. But finding an abundance of pigeons & popinnayes [parrots], they disdained any more to eat those great foules calling them Wallowbirds, that is to say lothsome or fulsome birdes.”
The “loathsome”–the “disgusting,” the “nauseating” bird–does not sound like “very good meat” and has led to some writers to claim that the birds were only eaten by necessity, and were just plain nasty. But van Warwijk goes on to explain the Dodo was called this “…for the reason that the longer and oftener they were cooked [i.e., “wallowed in the pot”], the less soft and more insipid eating they became. Nevertheless their belly and breast were of a pleasant flavour and easily masticated.” Sir Thomas Herbert in 1634 said “It is reputed more for wonder than for food, greasie [robust] stomackes may seeke after them, but to the delicate they are offensive and of no nourishment.” The one recipe I could find for cooking Dodo suggests it be done with mangoes, fruit native to Mauritius, so it would “taste like something.”**