360 grains on a 45 lbs bow means 8 gpp. That's about as low you can go for most traditional bows. The bow will tell you if she likes it. If it gets loud and gives more vibrations after the shot, she is telling you you are asking too much from her.
If it is a one pce longbow, I think you are a little bit to low in weight. If it is a three pce design, you could get away with it. The higher mass allows you to shoot lower weight arrows.
You could try to shorten the shaft a little and use 125 grains points. Be careful with shortening, carbon shafts are very sensitive for that, they will get a higher spine very fast. Just start with halve an inch max. each time. Fletching will add another 10 grains. A wrap also adds another 10 grains. Then you will move towards the 8.5 gpp, which will be a little bit safer for your bow.
For the deers it won't matter.