hi! welcome to the forum :wave:
I think everybody has a different opinion about it, and technically your vet is right, but for older rabbits, not babies.
in adult rabbits an excess of pellet can lead to weight problems along with dental problems, as they fill up upon the pellet and don't eat their hay, thus allowing the teeth to become overgrown and painful. the only way that can be fixed is by a dental, and unless the diet is sorted it will keep happening. a rabbits diet should be 80% hay, so you can see the issue.
but in younger rabbits pellets are important as they have nutrients in them to help them grow. protein, vitamins, without them they'd probably be malnourished and end up with issues later on in life. plus, they're growing, they need extra calories.
some argue unlimited pellet is good for rabbits, and others wouldn't.
personally - I'd argue unlimited (as in, literally, every time the bowl is empty filling it back up) is more harmful to their health than helpful. young rabbits can also get dental issues if they don't eat enough hay. many rabbits far prefer the tasty pellet over the boring hay, so they're more likely to just eat pellet. good hay eating habits are started at a young age (imho), often rabbits who haven't had a good diet at a young age don't want hay when they're older and it becomes a task to get them to eat it.
I made that mistake with my first rabbit, constant bowl of hay, and up he had his first dental at around 6 months old and was extremely tricky to get to eat hay in his later life.
however I wouldn't say they should be strictly rationed for a baby bunny. a vet nurse I'm in contact with suggest 5 tablespoons for your average rabbit (for a larger rabbit like a conti, she'd double that). I personally went with 1 table spoon per kg of expected adult bodyweight, so my mini rex Orion was expected to weigh 2kg as an adult, so he got 2 tablespoons. he's now a healthy adult with good eating habits for hay with no issues.
just like with most pets, everybody has a different idea of what is right. its about doing your own research, talking to other owners and seeking veterinary advise and making your own decision
personally I wouldn't advise totally unlimited pellets, as I feel good hay eating is started at a young age and can contribute to an early need for a dental when they're quite young. others haven't had an issue and found it to be fine, its complicated.
I'd also just like to say its great you got her vaccinated! there's a second one that she needs - filivac (or eravac, used for meat rabbits, immunity is 9 months). she can have that in 2 weeks. I just wanted to mention in case you didn't know