I know that you don’t want to pick up your bunny to check the gender, since most bunnies don’t like being held and you don’t want to scare him or her right away, but if it is a male of at least 4 months, you should be able to see his testicles. They look sort of like pink kidney beans. Sometimes you can dangle a treat over their heads and they will stand up to reach it, then you can take a quick look and see if any testicles are present. If the bunny is still wary of its new situation, it might not stand up, though.
No rabbit likes going to the vet, so your bunny may be a little mad at you or put out at you, but they will get over it, and there are times when they have to go to the vet. Have the carrier as close as possible and have a towel in it. Hopefully you can grasp her without a lot of struggling and get her right in the carrier. Be very careful when picking her up and try to keep her low to the ground if you can. Being up in the air is even scarier and rabbits can really struggle and can sometimes hurt themselves by struggling a lot. That is rare, but a proper, firm grasp is needed and getting them in the carrier as quickly as possible is best. They can also accidentally scratch the person holding them, or trying to hold them, if they struggle, so be aware of that.
I hope I’m not scaring you, you may be able to scoop up the bunny with no trouble and get it right into the carrier. Put some hay in there too. The bunny may not eat but it’s there just in case. That is the most important component of their diet.