Before, before, before!
It is so much easier, you have so much more time, freedom and flexibility.
Afterwards, one of you is looking after the baby at all times and yes, you can carry a young baby around while you house hunt but you will be more or less preoccupied with them. The more active they become, the harder it will be to schedule time together as a couple to look, plan, discuss, prepare. Possible but much harder than while you're just two adults.
Immediately afterwards, well, who knows. You or the baby could be in hospital for weeks or quite incapacitated. The baby could be a particularly bad sleeper etc. Hopefully not but, you cannot know in advance how things will be afterwards. You have to assume you are not available for other pursuits for a few months.
If you wait, you'll be waiting a while. A few years by the sound of it. That will scupper your, very sensible, idea of settling into the new area and meeting other parents through toddler groups etc who you can remain friends with throughout the pre-school years and potentially forever. If you're closer to family too, that is invaluable (if they're nice, interested and likely to be helpful), really worth their weight in gold.
I think you need to put the costs and benefits to your DH in those sort of terms. It is difficult to put a price on convenience, peace of mind, babysitting, a strong relationship between baby and family members from the start and a happier, more relaxed life. Their value is really, really high though.