Lenka, your bunny is absolutely beautiful. I have two ND bunnies and my doe is a little over 2 pounds and not quite 5 months old yet. My doe went in for her well check 2 weeks ago and my vet said he would not spay her until she was at least 6 months old. He said it can be hard to see the little lady bits in these small dwarf rabbits when they are so young so he prefers to wait until they are 6 months old. It does no harm to a young rabbit to wait until they are 6 months old to spay.
He asked what diet my doe is eating and I told him unlimited timothy hay, unlimited young rabbit pellets, a very small handful of alfalfa hay at bedtime, and greens. He said that was "excellent" and to start limiting her pellets and eliminate the alfalfa at around 6 months of age. Let me tell you, my bunny is a little piggy and she is probably eating way too many pellets right now but she is active and healthy so I'll follow his advice and start cutting back in a month. I would estimate that my doe is eating 1/8 cup, maybe even a little more, of pellets a day. I'm not recommending that amount, I'm just saying that's what mine eats and she is at a healthy weight, so it seems to me that a spoonfull of pellets for your little doe should be just fine. This is just my own opinion though, I am not a vet.
If you don't feel confident with your vet, maybe you can find a different one? I would imagine that he would have commented on her weight if your bunny was overweight. It would be a red flag for me though if my vet wanted to spay my bunny at only 4 months old. I would start looking for a much more rabbit savvy vet in that case.