I tend to actually make my first carpenter a wood cutter as well. The reason is, I usually want anyone not doing a secondary job mining right at the start so that I can get a basic fort cut out relatively quickly without having to rush it and be left with something I can't reshape into the proper fortress I wanna end up with eventually. I don't want to have one guy dedicated to carpentering, and then another cutting wood for him, it's too many people not mining or hauling.
Also, you don't need wood objects that quickly early on anyway. One guy doing both cutting and fabrication is enough to get your first set of beds, barrels and bins out and that's all you need anyway. Everything else like doors, furnature and what have you, should be made out of stone anyway since wood is far harder to come by. Your mason is the only person who you want doing only his secondary job of masonry pretty much at all times so that you can get important early stuff like workshops, dining furnature and office furnature built quickly out of stone. Everyone else I make pretty much a dedicated miner with one of them being my trader/clerk trained guy (negotiation, appraisal, etc), one being my stonecrafter to make goods to sell, and the other being usually a smith or clothier/weaver. Then I have my two farmers, one of which is a cook, the other who is a brewer. They serve as predominantly haulers in the early stages until their farm plots and workshops are ready. Sometimes I send them out to gather wild edibles early on too. Oh also, my mason or one of my miners is usally a mechanic too.
Most new immigrants, I put on mining duty before I train them in anything else so that they are tough in case I need soldiers. But anyone that I plan on using as a carpenter, wood crafter, or even some sort of funace operator or smith, I put on wood cutting duty for the same purpose, but so that they fuel their eventual secondary skilled trade.
