Hi there, welcome to HC
I'd use your first few days of owning her to have a good old mooch round the forum thread boards, and just chat gently to her while you're in the room so she can settle in. Moving house is a big adjustment for a tiny ham
Anyway, on to your question. Firstly, for the forest week or so, I'd wouldn't change or add anything to her diet 'til she's settled in. You don't want her to get an upset stomach. When you are ready to introduce veg, do it gradually, a small thumbnail piece every few days. And try and vary it. There are safe lists in some of the threads but always check if you're not sure. You can give fruit but it's a lot more sugary so give more as a treat. Hamsters will pouch their food if you give them enough but they'll take it to wherever their hoard is and leave it there. Of course, if they don't that it will go off an smell a bit funky in the cage so you just need to check their hoard and remove it if that happens. So if it's just a little bit they're more likely to eat it there and then. But they won't keep it in their pouch, if that's what you mean.
Can't wait to meet your little ham