Although wombats, especially young ones, look cute and are affectionate, full grown they can be aggressive, threatening, and even dangerous. Wombats are wild animals, not domesticated pets, and as such should be left in the wild where they belong. In most places in Australia, wombats are protected and it's illegal to keep them as pets.
Wombats need special care and a special diet. They're extremely strong and can be very destructive. They can tear holes in fences, doors, and even walls. There's not much that will stop a wombat other than concrete or steel.
As a wombat grows and matures, it becomes less and less friendly, and increasingly hostile and unpredictable. They have sufficient strength and speed to be dangerous.
Orphaned wombats are often taken in by people who have received special training to take care of native animals. They'll see that the wombat gets any medical attention it may need, and will raise the wombats until they can fend for themselves. The goal is always to release the wombat back into the wild when it's ready.
Keeping a wombat as a pet is in no way being kind to it. If you'd like to help wombats, there are numerous charitable organizations such as the Native Animal Network Association that you can donate to.
If you're interested in becoming a registered wombat carer, you should contact your local wildlife rescue organization or a local wildlife carer for more information. See the Emergency Wombat Care page for links.
If, despite that, you'd still like a pet wombat, why not adopt a virtual Wombie instead? Wombies are not only much easier to take care of than wild wombats, they won't get you into trouble and they won't destroy your home. And most importantly, the real wombats can be left undisturbed in their natural habitat.