It depends entirely on the county. Even what process you go through depends on what the judge and sheriff feel like doing.
In Albany Co, you have to appear before the judge to get a pistol permit. And you're not getting a carry. In other counties, it ranges from 6-12 months, contingent on a safety class. Up in Warren County, practically as rural as it gets, you can get a "Hunting and Target" pistol permit, but there's no way you're ever going to get a CCW.
In some counties, in order to buy/transfer, you have to buy the gun, take/mail the receipt to the sheriff's office for an amendment to your pistol permit, wait a while (I've had as little as 2 weeks, as long as a month and a half back in the Bad Old Days), get the amendment in the mail, and bring that back to the FFL.
In other counties nearby, the sheriff's office happily dispenses blank amendments--you buy the gun like normal, and drop off the filled-out amendment on your way home.
I would call around to some shops in the county and find out. Just because Syracuse is north of Suffolk County doesn't mean it doesn't suck out loud.
What I would not do is send the revolver up with her.
Another thing that can come in handy is a junk gun. Some counties require you to have a handgun purchased before you can even apply. So instead of plunking down $800 on a shiny, she can either pick out some $75 barely-working piece of garbage, or you can FFL said worthless piece of garbage to her. That way, while she's waiting on her permit, you guys have only got a cheap token gun sitting in the FFL's safe. When the permit comes through, then you buy/send the one you really want.