Most bunnies don’t actually like being picked up, though many will tolerate it, which is great when you need to clip nails etc. Just because a rabbit doesn’t fight or squirm to get down, doesn’t mean that they enjoy it. A fast heart rate and/or wide eyes can reveal that they are not comfortable, however, some bunnies absolutely do enjoy being picked up, but it is rare, and your cousin got luck if that is case. The fact that your bunny jumps on your lap to be pet is wonderful!! That’s also not all that common, so count your lucky stars for that sweet gift.
Your cousin also may get lucky with her bunnies being bonded, but her rabbits are reaching sexual maturity, and it would not be unusual if they got aggressive with each other over the next few months. So tell your cousin to keep look out for that as they can really do damage to each other.
I also believe that waiting until your bunny is spayed is best. Especially because of the age she is reaching, even if she’s not aggressive, the scent she’ll be putting out right now can bring out territorial behaviors(aggressive and/or messy) even in another neutered rabbit.