The point of trying to get the vaccines done fairly soon is that there's no way of knowing when your daughter might come into contact with any of the diseases. It would obviously be a shame if she was on a very gradual schedule and ended up catching measles, whooping cough or what have you while she was waiting to get the vaccine, hence trying to get them done in the shortest possible space of time that will still give her body time to mount an adequate response.
Although it sounds like a lot, it actually isn't when you look at it on the immunological level. This is because vaccines these days contain far fewer antigens than live viruses/bacteria, so even vaccinating against multiple diseases in a short space of time requires only a tiny fraction of the response from the immune system that, say, fighting off pertussis would. She's therefore better off getting the vaccines on a rapid schedule to give her protection ASAP, in order to avoid a possible situation where her body might have the far greater stress of fighting against one of the diseases.
It's actually quite feasible for her to have the MMR and the DTaP at the same time (as I said, the number of antigens involved is extremely small compared with what the immune system has evolved to be capable of dealing with) or with any interval in between, as they don't seem to interfere with each other - see https://www.gov.uk/government/upload...er-21-v2_0.pdf
, page 215. So she doesn't need to wait a month between each shot. However, according to the same source, she should wait a month between each DTaP shot and three months between the two MMR shots (and Japonica is quite right - it should be only two MMR shots, so I don't know why you would have three on the schedule?)
Edited to add: And I forgot to say that she'll also need a DTaP booster, so your doctor will need to schedule that in there, which seems to be about 6 - 12 months later.