Basically, if late Ming/Qing China had the political and economic willpower to pursue a navy (say for this scenario, a European-backed Kingdom of Tungning poses a more credible threat that OTL, although this question applies to any number of PODs that could have revitalized Imperial interest in naval affairs from the 16th century onward), could they have built wooden ships armed with cannons that could have contended with 18th and early 19th century frigates and ships of the line (in similar numbers) in the surrounding vicinity of mainland China and Taiwan?
From historical examples, there have been junks able to rival even first-rates in size and displacement, such as the treasure ships (even with the most conservative size estimates). Indonesian great djongs were also said to have been impervious to 16th century Portuguese bombards while also carrying upwards of a thousand men. However, at the same time, the great djongs were also criticized for their maneuverability, and the treasure ships were presumably not better off either.
As for woods, southern China had teak, which is a fairly good wood for shipbuilding, and I believe there also cork oak variants throughout central and eastern China too.
From historical examples, there have been junks able to rival even first-rates in size and displacement, such as the treasure ships (even with the most conservative size estimates). Indonesian great djongs were also said to have been impervious to 16th century Portuguese bombards while also carrying upwards of a thousand men. However, at the same time, the great djongs were also criticized for their maneuverability, and the treasure ships were presumably not better off either.
As for woods, southern China had teak, which is a fairly good wood for shipbuilding, and I believe there also cork oak variants throughout central and eastern China too.