1:30 PM PT -- The Columbus County Sheriff's Office just told TMZ they, along with the Columbus County Animal Control, have "initiated a joint investigation into allegations of animal cruelty. The investigation is ongoing."

1:11 PM PT -- A source close to Jenelle tells us right after Nugget nipped at his daughter, David brought the dog outside and continuously slammed him against their back deck ... from there, he took Nugget into a wooded area and shot him.

12:07 PM PT -- Law enforcement sources tell us Animal Control officers just went to Jenelle's home to do their check. We're told officers were able to drive onto the property through an open gate, but there was a grey pit bull on the porch and several "No Trespassing" signs.

Our source says the Animal Control officers -- fearing for their safety -- left the property and alerted the Sheriff's Department who, we're told, will now attempt to complete the visit.

We're told officers want to determine if Nugget is alive and whose name is on ownership papers for the dog ... from there, they'll be able to determine next steps.

Animal Control wants Jenelle Evans and David Eason to answer some questions about the death of their family dog, but that might be easier said than done ... based on David's history with unwanted visitors.

TMZ's learned that following the news that Jenelle's husband shot and killed her French Bulldog, Nugget -- for nipping their daughter, Ensley -- North Carolina's animal welfare hotline was flooded with calls about the incident.

We're told the Attorney General's Office received 138 complaints and referred them to Animal Control after review, and also informed the Columbus County Sheriff.

Sources connected to the case tell us Animal Control is sending an officer to the 'Teen Mom' couple's house Thursday with a mission -- confirm the dog is dead, and verify Jenelle and David have possession of the dog's corpse.

It's unclear what, if any, legal action could be taken after that -- but it likely won't be an easy visit for Animal Control. Eason reacted aggressively when authorities showed up at his home in December.

As we reported, he posted a series of gun-crazed videos after he said Secret Service drove up on his property to question him about some threatening social media posts. He said he wasn't afraid to shoot future trespassers ... and showed off his stockpile of ammo.

David's alarming behavior reached a new level Wednesday, when he practically admitted on Instagram to killing Nugget. Jenelle later confirmed it, claiming David dragged the dog into the woods and shot him.

Up to this point, David's gotten away with it. The Columbus Co. Sheriff's Dept. made it clear the only way they'll take action is if Jenelle files a police report. We were told they don't rely on "sensationalized" social media reports. We'll see if a report from Animal Control will change their mind.