In my opinion..., 6 weeks is probably the hardest age to pull a calf and get it to do much. Not really big enough/ready to wean and go on all feed and hay, too old to put over on a bottle, but it still would benefit from milk. I would put the cow in a small lot with the calf and supplement with feed and the calf will start eating more feed if it is not getting enough milk from the cow. Then in a few weeks when it is eating more, it will continue to eat when you pull the cow.
My oldest nurse cow went off feed right about when her calf was 6 weeks and she had 2 others on her. Long story short, she has tumors and the vet gave her a VERY POOR chance to live out the week. After about 2 days, she perked up so we went the Dex route as a steroid to see if I could get her past what I consider the awkward stage of 6 weeks. I pulled the one calf I had put over on her because it had been a bottle calf and was older when I grafted it on her. It was eating grain and hay pretty good, so just left her own calf and the other one that was 3 days old when I put it on with her own.
That was nearly a month ago. She has rallied, has had dex a couple of times when she seems a little slow or walking like she is hurting. She is raising the 2, out grazing, and getting grain once a day. The calves look much better than they did at 6 weeks and are coming in the creep gate for some grain also. I am very glad that I tried to keep her going past that 6 week period because the calves would have suffered. I didn't have another nurse cow to switch them over to or I would have and I would have put her down. Since she has rallied, she will get to have as much time as she can until she gets in bad shape and then I will put her down.
So, I would put a poor doer with her calf on a little "increased ration" if the calf is at that stage and get it eating more. But I normally will pull the calf as a baby if the cow doesn't seem to be making much milk...and they don't get a second chance to be a poor producer again.