“It happened in the middle of our Sunday carvery serving so it was all very busy”
The female reportedly leaped over a fence at about 3pm and was last sighted on the Gortin Road that evening.
Members of the public have been urged to approach the animal with caution.
Richard Beattie of Glenpark says while the animal poses no real threat, it may be startled and unpredictable.
He pointed out the wallaby was out of her enclosure and in an area that would be strange to her, but stressed they are quiet animals. She is described as around two-and-a-half feet tall.
“Just stay back, phone through to Glenpark and we will rescue the animal,” he told the BBC.
The search remained ongoing today, with Mr Beattie telling the PA news agency there were thousands of acres to search.
Wallabies belong to the same "taxonomic family" as kangaroos though are much smaller in size - there are around 50 sub-species of wallaby and four kangaroo.
Richard told BelfastLive he has issued an appeal for anyone who may come across the wallaby to get in touch with him at Glenpark Estate.
“Two wee wallaby kangaroos came yesterday, they came about 3pm and we put them into the enclosure,” he said.
“One of them jumped over the enclosure and the last time it was seen was a quarter of a mile down the road from the estate. We’re still looking for it now.
“It happened in the middle of our Sunday carvery serving so it was all very busy.
"I got a call from the groundsman to say he was away.
“Hopefully we will be able to find him. He went in the direction of Omagh.”
There have been no further sightings but Richard is hoping that by getting the word out somebody might come across it.
“It’s just a matter of where and when. We have a good enclosure here but something must have just startled them.”