I just have two Jersey cows so far, a third due to calve for the first time in August. So I have limited experience to share - but Hillie, the original and 'matriarch' of my little herd, produces way too much milk for just one calf, especially a Jersey calf. Even if I kept her on restricted/poor grazing and didn't give her any cake, I suspect she'd just get thin and still produce more than one calf could drink. When the calf is older it'll drink more, and a beef x calf will have a bigger appetite than a pure Jersey, but early on in the lactation, she'd certainly need either a second calf or for me to be milking several litres off her every day.
Plenty, Hillie's first daughter, now on her second lactation, would be easier to manage and probably could cope with just one calf. I have often wondered whether she is less bounteous than her mum because I didn't rear her for record-breaking lactation, whereas I bought Hillie as an in-calf heifer from a dairy farm, so of course she had been reared to produce as much as possible. I can get more milk out of Plenty but she needs feeding to do it, whereas Hillie always produces a lot of milk and just loses condition if she doesn't get enough feed to support her production.
Hillie produced even more milk in her third lactation, and dairy farmers do say that they hit their peak at this point - if they are going to go down with milk fever, it's often on the third lactation. So even if your girl manages with just one calf the first time, she may need some help using her milk later on.
If it were me I would plan to get one calf to suckle your girl alongside her own calf this first time. You could probably wean the add-on at 3 or 4 months if you want; by that time her own calf should be able to drink enough to keep her comfortable. (Depending on her productivity, and how good the grazing is by then - if it's a good summer you may still struggle!) I take it you are not wanting to milk her yourself?