Hi bamabow, I can say "nice choice of gun" because a lot of us have one. I've been shooting the .44 Mag from a Ruger Bisley Hunter 7.5" for whitetails for about 6 years and am really happy with it. I've had my best results with my own loading of a 240 gr. Hornady XTP and H110 powder. But if you don't reload (yet) no problem you can find good commercially available whitetail loads (some with that bullet). The 7.5" barrel gives it the velocity you need to make the bullet perform for whitetails.
I use a Bushnell 2-6x32 pistol scope rather than a red dot. This was (at least at the time) the only pistol scope I found that holds very close to the same eye relief across low to high power. With it, I have confidence (and have killed deer) out to 75 yards, but then depending on my rest or lack of same, and deer angle, I'm good to 100 yards. But I'll defer those shots if I can get to 75 or less.
It's a heavy gun and it barks quite a bit. It took me a while to be able to shoot well enough to have the confidence to get out there with it for the first deer. So I'd say it's best to start shooting it early so that come the next season, you're hitting tight groups at distances and angles you expect to meet deer.
Best of luck!