She sure is a cute little doll - I am glad she's doing well.
It's been a million years since I had such young one on the property so I didn't know the vets like to wait until they're a little older to vaccinate for tetanus.
I think, in your filly's case "to wrap or not to wrap" has to be a judgment call and flies play a big part in that.
If she is in a clean environment (not standing in dirt or mud all the time) leaving it un-wrapped with antibiotic on it might be ok, some of the time.
But babies lay down a lot, so she could fill that gash up with dirt in the blink of an eye, plus your flies are bad. Wrapping is probably the best thing, which is what your vet wants for now
This is further to the comment I made on another thread that all horses are born with a death wish --- if not for themselves, for their owner. Your filly probably got that gash on nothing more than air. Where is the bubble wrap when it's needed