A lot of people train their bunnies to hop into their carrier when needed, so you could definitely do that. Usually all you need to do is feed them their pellets in the carrier, or give them a treat for going in it. It helps to leave the carrier out all the time, so they don’t get taken to the vet every time they go in it.
I do think it’s important to be able to pick up your rabbit though, because in an emergency he might not want to go into the carrier.
I tried to film my technique in this video. https://drive.google.com/file/d/12iIW-I7CAJIK7Zah6jN0470eQkOlaqr3/view?usp=sharing
It’s not the only way to do things, but it works well for me and is a safe way to carry a bun that minimizes their stress. It also works well for putting a bun into a carrier, because you can angle them bum-first so their feet are less likely to catch on things. This is at a rescue, and the bun in the video HATES being picked up and doesn’t like to be petted when she knows she’s going to get picked up soon. Typically, it is best not to chase the rabbit. I don’t actually like how quickly I was following her, but I was putting up rabbits at the end of the day and it was pretty busy. When I had more time, I liked to sit down in the pen with her and just wait for her to settle on her own. Then, if you approach from the side, they are less likely to run away. I will press one hand on the top of the head and shoulders. Then that hand transitions to hold the front end, and scoop with the other hand. I am using what’s called the “football hold”, which works very well for squirmy buns and tends to help them feel secure.
How long have you had your bunny? You can also work on desensitizing him to your hands by hand feeding, and spending time on the floor with him. You could even train him to “target” to your hand with clicker training. You might want to work on those types of things before trying to pick him up too much, so he doesn’t only associate your hands with being scooped up.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.