Carpentry is no different than any other class; recipes at level 8 require just as much synthesis and quality to complete as recipes of the same level in other classes. This means that if basic synthesis isn't doing as much as you expect, then one of two things must be true: Either you don't have enough gear with Craftsmanship on it (don't forget your off-hand tool!), or it was just as bad at this level on other classes, and you've just forgotten how bad it was.

There's rarely a "need" to grind. Leves will level you up fast, especially if you focus on HQing lower-level Leves rather than NQing higher level leves. If you've run out of level allowances, yeah, you might need to grind - but if you do, grind lumber. Save the HQ lumber you grind in order to more easily HQ items for sale and for leves, and sell the NQ lumber for higher-level crafters to buy who don't care about HQ vs NQ ingredients.

At your level, too, I might suggest swapping out Manipulation in exchange for Steady Hand II. That extra 10% success rate is very noticable when spamming Hasty Touch at low levels to make up for your small CP pool. Master's Mend will suffice for now.