I would get started milking her as soon as she freshens. Make sure the calf gets a good two or three feedings of colostrum and if you didn't see it, bottle or pail feed the calf to be sure they get that good start.
The calf is not going to take much milk early on, and the cow adjusts her production to the amount of milk being taken. So the 3/4 of a gallon you want is not necessarily a small amount of her production. You need to be milking her at least once a day to continue to build her production even while the calf is sucking. She's not going to produce huge amounts of milk
just because she is genetically capable of doing so, or because you feed her a lot of grain. They base their production solely on how much is being removed: You and the calf milk her out, she produces more.
Don't look at it as "I need 3/4 of a gallon a day". Look at it as "I need milk for the next 9 months" and to get that you need to push the cow to milk for you now so that she peaks in production in the next 6-8 weeks. So you'll be getting a lot more than the 3/4 gallon for awhile, but you have to do that to get the 3/4 gallon you need 6 months from now. And remember during this time that the calf is tapping more and more milk for the next few months as well. They can take HUGE amounts of milk when they are nursing off the cow, a pint or two at a time all day long.
Time to learn how to make butter and cheese, is all.
ETA: About the mastitis. Don't worry too much about it in a new heifer if she's been in a clean environment. It can happen but it's not that likely. But keeping her milked out promotes udder health. When you milk her, don't leave a quarter for the calf, for example, make sure you milk her out evenly all four quarters. The calf can be clean up batter for you (or you for the calf), and both of you will keep her udder cleaned out and healthy.
Jennifer