Hi there nalufish! Welcome to the forum!
So is this your first fish endeavor? Have you read through the sticky articles we have around the forum? They give the basics and teach you all about Betta fish!
So there is this really important thing called the Nitrogen Cycle. Basically, bacteria build up in their favorite place to hang out (the filter) and they convert all the bad stuff (ammonia and nitrite) into much less harmful stuff (nitrate) which can be removed with a water change. It takes about a month for the bacteria to to build up though, during that time, ammonia and nitrite can (and should) get high and dangerous to the fish. Here's a sticky about the Nitrogen Cycle in general:
So what you'll be doing is called a Fish-In cycle, it's pretty easy to do provided you keep an eye on the water and make sure the ammonia doesn't get too high, but it's very doable!
Here's another good article to read through that will help out, good guidelines to follow when doing a Fish-In cycle:
And this is just the basic stuffs that you can read through at your leisure
In total; yes, you should put her right into that tank. Make sure you acclimate her! If you do not know how I suggest you look at videos on youtube on Drip Acclimation, it's my preferred method and is very easy on the fish, especially when making a big change! You can also use plastic cups (generally we keep the cups from PetCo/PetSmart they come in for this use) and scoop her out of the bowl and float her in the new tank for 10-15 minutes, add in a teaspoon or so of new water to the cup, dump out part of the water when it gets too full and keep doing it for a total of 20-30 minutes depending on how drastic the changes are. I usually add in some water every 3-5 minutes or so during that 20-30 min period so they can adjust.
I think I covered everything...Oh! Do you have a heater as well? Did you buy a kit?