I'd say it really depends on what matters most to you! Having your gynae there is definitely a comfort thing, some mums I know really valued that continuity, especially since your pregnancy has been smooth sailing so far. That said, 38 weeks 5 days is still a bit early, and a few people have mentioned that inductions at that point can sometimes mean a longer labour or a higher chance of needing intervention, even when everything's been fine up till then. On the flip side, if your gynae won't be around and you're keen to have her deliver you, the risks at 38+ weeks are generally quite manageable.
I think the honest trade-off is this: you get your preferred doctor, but you're bringing forward labour by about 10 days when baby's doing well. Some mums felt totally at peace with that choice, while others wished they'd waited and seen if labour came naturally. Since your pregnancy has been uncomplicated, it's worth asking your gynae exactly what the medical reasoning is beyond her schedule, sometimes there are subtle factors she's spotted, and maybe also asking what happens if you wait and she arranges another doctor you trust to cover your delivery. That way you're making an informed call that sits right with you.
Definitely have a good chat with your gynae or get a second opinion from another specialist if you're unsure, it's your body and your birth, so you should feel confident either way!