3:20 PM PT -- Jenelle spoke with US Weekly about the incident, saying, "He just took her and shot her in the woods, about two acres away from the house."

As we reported, local law enforcement said they won't act on the killing until Jenelle comes to them to report the crime ... one source we spoke to said media reports and social media postings aren't enough to trigger an investigation.

Jenelle also told US, "At this time, we are dealing with this rough situation. I want to focus on what's best for me and my kids."

9:45 AM PT -- Police went to Jenelle and David's house Tuesday night to perform a welfare check on Ensley. Officers found everyone, including Ensley, was okay.

As for the dog -- a law enforcement source tells TMZ ... David told cops Nugget was alive, although he would not let them see the dog. We're told cops have no evidence showing anything happened to the dog.

The Columbus County Sheriff's Dept. says it's contacted Animal Control, but as far as any further investigation from cops ... our source says Jenelle would need to make a report on her own. We're told officers won't act on "sensationalized media reports or social media posts." The source said it's irrelevant to cops what Jenelle says on IG.

Meanwhile, PETA says it hopes charges are filed against Eason if it's true he shot Nugget. They say, "People who abuse animals typically don't stop there."

"Teen Mom" star Jenelle Evans is heartbroken over the death of her dog, which was shot and killed by her husband ... who is defending his disturbing move in the name of protecting his family.

David Eason admits he killed the family's French bulldog, Nugget, because it bit the couple's 2-year-old daughter, Ensley. He shared a video that appears to show the dog snapping at Ensley as she's moving closer to its face for a kiss.

David explained his decision to put the dog down, saying ... "I dont give a damn what animal bites my baby on the face... whether it be your dog or mine, a dog is a dog and I dont put up with that s**t at all."

A photo of Ensley's face after the incident shows a red mark, but there's no apparent break in her skin.

Eason added ... "I'm all about protecting my family, it is my lifes mission. Some people are worth killing or dying for and my family means that much to me. You can hate me all you want but this isnt the first time the dog bit Ensley aggressively. The only person that can judge weather or not a animal is a danger to MY CHILD is ME."

Jenelle doesn't seem to be on the same page as her husband at all. She just shared a photo of Nugget sitting in the car with her, along with a message suggesting she believes they should have simply trained the dog to stop biting.

She wrote ... "Nugget... I'm crying everyday. I love you so much and I'm so sorry. I'm speechless," and added, "You still had a lot to learn and a lot to grow from your lessons."

Jenelle says she's heartbroken and distraught, and there are reports she fled their home after the incident.