How does the professional class fit into Marx and Engel's class struggle theory? I know that in the first part of The Communist Manifesto, Marx and Engles discuss at length the relationship between the Bourgeois and the Proletarians. The former being the owners of the means of production and the latter being the working class that is engaged in a struggle against said owners.

However, after reading the first part of the manifesto I can't figure out where "Professionals such as doctors, layers, accountants, nurses, etc. fit into this model. While they aren't the owners of the means of production for physical goods they posses special knowledge that allows them to charge a premium for their services. As such, members of the professional class generally aren't viewed as struggling workers. 

Why wasn't this class of worker included in the Communist Manifesto and where do they fit in with Marx and Engel's theory?
Marx's discussed struggle had less to do with your income-position in society and more to do with how you derive income, whether through profits, wages, or rents. You bring up a fascinating issue with his analysis and the solution is all about framing. Even doctors end up selling their labor on the market (in increasingly specialized components). While the labor of a doctor is different than say a machinist, their income is fundamentally different than that of someone who owns the means of production. The 17th century putting- out system would be maybe the clearest split between the two.  Keep reading Marx! Eric Fromm has some great essays that explain the nuance in Marx's world view. Hopefully this answer helps