tips and notes:
Another way to express wanting something is to use the verb teastaigh (to be wanted/needed), followed by a version of ó. Written this way, Teastaíonn bia uaim is the alternative way to say I want food; it can also mean I need food. (A literal translation would be "food is needed from me".)
Teastaíonn na leabhair uaithi She wants/needs the books
Teastaíonn seacláid uaimid We want/need chocolate
Teastaíonn uaim snámh I want/need to swim
Teastaíonn cáca ó chailín A girl wants/needs a cake
An dteastaíonn na hataí? Are the hats needed?
I just copied the text from tips and notes ;-) However, I think, this is an excellent observation.
Normally the preposition would come after the noun (pardon: "subject"), however a verbal noun (snámh, ithe ...) should come after the preposition.