One-month baby at high altitude

I have gone on hikes with infants as young as yours, at sea level and
at altitudes as high as you mention.

As far as the baby's oxygenation is concerned, I would expect no
effects of the altitude. But take extra care to keep the baby well
hydrated and avoid sunburn. If the birth mother will be hiking,
consider her physical fitness level and post-partum status. At 4
weeks postpartum many women still have incontinence problems. Also,
if she is nursing, she will need extra water and calories.

Bottom line: If hiking is not something you do normally, don't do it
with a small infant. Also consider the quality and accessibility of
the trail. Does it involve scrambling? Risk of rain or other bad
weather? Difficulty of extraction if you are injured and need to be
carried out in a litter?