In reply to Ling:
Congratulations! Hope you stockpiled your sleep!
When we had our first one, getting to the wall was easier (once the Mrs had recovered enough to climb) as they sleep so often and even when they're awake, do so little, that it's easy for you either to tag in and out, or even both climb - assuming you can leave the cot somewhere in sight but out the way.
(Note, this is bouldering only, wouldn't want to be tied in personally)
As soon as they started being mobile however, it was no longer safe (or fun!) to go to the wall, not least because you were either getting frustrated shepherding them OR the baby's frustrated as they want to explore.
So at this stage, we just took in turn to go to the wall - though this massively depends on your baby. My wife breastfed both of ours exclusively for the first 12 months, so couldn't really leave me with the baby for three/four hours as I couldn't feed it. Bottle-fed babies won't have this inconvenience!
Lastly - if you can - pick your walls. We personally weren't concerned about chalk in the air, but both of our locals (Craggy 2 and White Spider) seldom get too hazy. But, when we were tag-teaming, White Spider was a nicer place to hang out when not climbing (though Craggy is our preferred centre for setting, atmosphere and so on).