4.9 is very little, but if the paed has prescribed so young, they must have considered the potential benefits closely.
A trial period is fine. No one says if you give her the medication for a month and see what the outcome is that she has to be on it until 18. It might not work anyway
If it doesn't work, it's an easy decision - she doesn't take it. If it does work, then you need to weigh up the benefits and consider any other issues (there is no particular reason she will suddenly have a personality change). It might be helpful for your dh to read some accounts written by older children who have successfully taken medication and been able to live their lives.
Ds tried one med and it had no effect, he now takes Vyvanse. He said it helps him control himself - he no longer feels as though he has no control over his own behaviour - it gives him the option to make decisions, as opposed to feeling out of control all of the time. He didn't take meds until 10 though.
I assume that you have exhausted the omegas/ zinc/ magnesium supplements route prior to seeking medication? It works v well for some - ds's teacher when we started the omegas/ zinc/ magnesium asked us if we had started to used ADHD medication as he was like a different child in terms of concentration and sociability (ie he was able to do both!)
4.9 is very little though. As is any, I assume as they considering medicating at this point, there has to be a reason for it, in terms of personal or peer group disruption. I'm not a fan of school dictating medication choice, btw. It smacks rather of the need to externally control without effort... Unless of course they have been working hard with you family over a period of years to put in other supports (1-1, small group work, behaviour plans). And at 4.9, that seems unlikely.
Can you explain what issues she is having at school? I assume she has only been there a couple months?