I suspect that your proposal is not viable, at least not without significant deviation from the typical idea of humanoids.
The main problem: women are already at the limit of walking effectively while still being able to give birth to such big babies. C-sections are already a rather common operation for several reasons, one of which is the non-trivial risk that the baby will be too large for birth to be safe for mother and child. Widening the hips might sound like a good idea, but doing so seriously compromises the ability to walk upright at any reasonable pace. If you want women to be limited to waddling around slowly like penguins, it might work, but in nature they would be easy prey: natural selection would weed that out rapidly.
For egg-laying humanoids, the egg needs to be large enough to contain the baby when it is ready to emerge, which by necessity means one of two things. Either the baby will be born even less developed than human infants already are, with a probable spike in stillbirths and birth defects (likely including reduced intelligence), or the egg needs to be even larger than the baby would be, with a probable spike in maternal mortality as mothers die from laying these giant eggs. Pick your poison, but either way I don't see that ending well. I suppose evolution might provide an answer along the lines of temporarily widening the hips, narrowing the negative impact on walking and running to a day or two before and after childbirth (not ideal, but manageable) while still allowing giant eggs; it's worth considering, at least, although the necessary structure to allow that would probably come with other effects on the hip bones (I suspect that they'd be thinner and/or more fragile, since they'd have to be able to shift around).
Another problem: egg-laying is actually more demanding on the body than pregnancy. This might seem counter-intuitive, but you have to recognize that the egg is effectively a self-contained womb. If it's going to nurture the growing child within, it needs to hold all the necessary nutrients, calories, and so on that it will need, and the mother's body will have to provide that. Moreover, the mother's body will also need to produce the material for the eggshell (which is presumably not going to be of much nutritional value, unless the infant tries to eat the thing when it hatches), which would not be necessary in a pregnancy.
The burden might be a shorter duration, perhaps three months to produce the egg so that it can sit around for another six months somewhere suitably warm, but it's overall going to require more resources, more energy, than the usual mammalian pregnancy and live birth. There's also the question of whether the human body could even produce such an egg materially faster than nine months: I don't have a certain answer, but if it's no, then there'd be no point in laying an egg that would hatch within a day or two. Nature is ruthless when it comes to selecting for energy efficiency: there's several reasons why no animal (to my knowledge) that evolved to give live birth has ever returned to egg-laying, and that is a big one.
Problem three: this has more to do with the evolutionary background, and you could bypass it if you wish just by stipulating that live birth never evolved in your world (the effects of that on your worldbuilding are left as an exercise, but I'll warn you that they would be considerable). Pregnancy and live birth, overall, is generally superior to egg-laying as a practical matter. Egg-laying itself demands more energy than a pregnancy would: I've already explained that above, but that's not the only point.
Eggs have to be incubated and protected, unless you want to lose the great majority of them and thus waste significant energy on producing those eggs; this works when the investment per egg is small (fish, insects, basically most small animals that don't fly), but that lack of caring for one's young is not conducive to social behavior or the development of human-like intelligence, and humanoids would be investing too much in each egg in any case. Incubation and protection of an egg or eggs generally entail one parent spending most or all of their time guarding the nest (or both parents taking turns), which means a lot of time and energy that could have gone instead to other needs, especially finding food; in a pregnancy, both parents are left free to hunt without significant incapacitation (humans are an outlier here, but human women are usually still fit until late in a pregnancy or possibly even until labor begins), and protection is reduced to the mother ensuring her own safety, as would be obviously necessary in any case.
One more thing: the strain of producing the egg is still going to look and feel an awful lot like a pregnancy, and come with most of the same effects and complications. The mother's belly is still going to be growing larger as the body gets to work on that egg. Most egg-layers we know don't breastfeed, but most egg-layers we know hatch out young that are significantly more developed physically; as a practical matter, your egg-layers will probably still have to breastfeed to give their hatchlings enough nutrition, given how human babies don't even have teeth for a little while. If your end goal is to reduce the net strain on mothers, moving to egg-laying isn't the way to do it.
My conclusion: even if your egg-laying humanoids existed, conventional mammalian humans would have won the battle of natural selection by a significant margin.
None of these problems are necessarily impossible to solve, but you're going to have a noticeably different social structure, physiology, and so on than conventional humans do. It would definitely be interesting to read as a story, if done well, but it would require a lot of thought to do it thoroughly.