Pumping Confusion

I'm a FTM, and the notion of pumping is confusing to me.

My LO is 1 month 1 week old, and exclusively breastfed. I want to start pumping so her dad can start to feed her on occasion, but everyone is telling me something different as to when I should start.

Currently she eats every 1 ½ to 2 hours during the day (she's a terrible napper or she'd go longer). At night she'll go 3 or 4 hours, but it's not consistent, and I don't want to pump only to have her wake up immediately after wanting to eat (I already have oversupply/overactive letdown issues as is).

So I guess I'm wondering if I should start pumping yet, and when would be the best time to do so. Any help would be appreciated!