It’s natural to be weary about needles and injections, but even so, yes, it is scary to think about for your young rabbit! Thinking about stress levels and the effects is a good mindset to have.
Thankfully, vet care for rabbits have come a long way when going to rabbit-experienced vets. Giving shots and getting blood samples are sometimes required, as BH mentions. Some countries require vaccines, and wherher it’s baseline or critical testing blood work, those are done pretty routinely.
Now in terms of urgency, I think the only risk of not doing it now is miss detecting any sort of early detection of genetic issues perhaps. Blood work can sometimes reveal infections, poorly functioning organs, etc.. usually however, owners see symptoms then do a test, because blindly testing at random intervals is costly and probability, especially for younger rabbits, is low. There are always exceptions, but a part of me wonders if detection of problems that occur so early on and don’t show signs would indicate something treatable. This is all just my thoughts though, no medical training.
So my gut is it’s not necessary. If you have the funds and want a baseline, which is useful to have eventually, than that’s fine though! If the vet is experienced, it should be very minimal risk to your rabbit.
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.