These half-rabbit half-antelope creatures stand a little over 2 feet
long when fully grown and have horns like a deer growing 1 to 2 feet
Something to consider is whether the Jacklope has horns or antler. These are two different things and will heavily impact how the Jackalope behaves. My answer tries to cater for both scenarios.
The hare can grow to 70cm (2.2ft) which is approximately the size of the Jackalope. A rabbit at full size compared to a hare (or in our case a Jackalope) is considerably smaller, especially when you weight in the upgraded bone structure, muscles and the fact that the male Jackalope has horns/antlers up to 2 feet long on his head! So a rabbit looking up to a Jackalope is going to be scared.
Male versus Male
The Jackalope typically fights other males as you might have guessed. Horn on horn, the Jackalope fights other males to display dominance over his colony and typical fights usually last a few hours. The Jackalope who exhausts first loses and is outcast by the colony, providing they do not die during the battle.
Jackalope will only fight during mating season, when their antlers are fully grown. They have a free for all, male vs male all fighting for the idea mate. The same principles apply that after the battle the losing Jackalope is outcast from the colony, or doesn't get to mate easily, perhaps even at all that season.
Teeth and Legs
Jackalopes also have a few other tricks up their fur, they have razor sharp teeth and tremendous strength on their hind legs. Jackalopes use their rear legs to attack other males. During a male versus male battle, spectators (particularly other males) interpret this as a display of desperation rather than strength, and is usually only used as a last ditch effort.
Teeth on the other hand are a rarely used attack, this is due to the large size of their antlers/horns. It is very rare that another male will be able to get close enough to bite their opponent, especially without receiving some kind of reciprocating attack. However when they do; their long teeth penetrate into their opponent causing a deep wound. This wound leads to some blood loss, but is typically not fatal. In longer duels however, with hearts beating at maximum, blood loss becomes a very serious problem.
Male versus Female
Males do not attack the females, however females do attack the males. If the male in question has defeated the females mate the female will attack using her razor sharp teeth and powerful kick.
The male does attack back but only in self defense, should he feel threatened. The male will refrain from using his horns/antlers out of respect for the female, and he will instead, use kicking to push her away or hurt her enough to make her think twice.
Intentional or not sometimes the male kills the female. When this happens the other Jackalopes lose respect for the male and outcast him from the colony.
As you might have guessed Jackalopes are a respectful species.
Male versus Predator
The Jackalopes predator would have to be fast, a cheetah would be a good animal to use as an example. The Jackalopes cannot out run a cheetah but can make much more precise and agile movements, this is where the Jackalope really shines.
When attacked by a predator the Jackalope runs, it makes fast movements left and right to keep the predator moving its head. As the Jackalope does this it scans the area ahead for any chance of escape. Since the Jackalope is about 2 feet long it can fit in some small spaces (this also depends on whether the Jackalope is male/female and if they have horns/antlers) depending on the environment they live in, let's assume woodland, much like the image below. By darting left and right the predator has to follow it similarly but if the predator stops paying attention for just a second the Jackalope could have quickly darted behind a tree or through some bushes confusing and disorientating the predator.
Because we are assuming woodland there is the possibility for logs, burrows and bushes to hide in that are much too small for a larger predator to fit in. Should a hiding place not be available the Jackalope will run until it begins to feel tired, at this point it will slow down and wait for the predator to get closer. The female will wait until the predator is very close and will the attack using its rear legs, aiming for the head as much as possible. With such fast and powerful attacks to the face, the typical predator either backs off or pushes through the attacks. This type of attack however tends to lead to being eaten more often by predators.
The male on the other hand uses a similar tactic, except he has horns/antlers. When the male Jackalope turns around to face his opponent he becomes a bigger problem than the predator initially thought. With 2 foot long horns/antlers in his face it becomes a lot harder to grab him where it hurts. He will then use his horns/antlers to attack his opponent by ramming and swiping at his foe.
The male Jackalope is known to intervene should he spot another Jackalope under attack, although typically the male Jackalope will attempt to rescue females over other males.
Because the Jackalope is 2 feet long the risk of aerial attacks are small to none, (unless of course this isn't based on Earth as we know it) so we can rule that out. The same goes for aquatic threats, unless the Jackalope is living near water large enough to house potential predators, they shouldnt have any problems there.
The typical rabbit is scared of the male Jackalope, although it is known for male rabbits to mate with female Jackalopes and vice versa. This is frowned upon by the colony and is a very rare circumstance however rabbits do not care and are always trying it on.
The male Jackalope spends most of his time somewhere near his mate, if the Jackalope does not have a mate then he spends most of his time trying to win one over, especially in mating season (Some Jackalopes have been observed to have died from exhaustion from not resting in an effort to find a mate).
This means that when rabbits try to invade their territory there is always a male close by to fight them off. Due to the Jackalopes superior strength and size the typical rabbit runs away whilst others fight but ultimately lose having achieved nothing.