Quieres and lleve don't refer to the same person. The meaning of this sentence is "Do you want me to bring something?" Another possible meaning is "Do you want him (or her) to bring something?" as "lleve" is both first and third persons singular. In Spanish, whenever a pronoun (yo, él, ella, etc.) is omitted, it can be clearly identified from the context. "Do you want to bring something?" would be "¿Quieres llevar algo?" 加油！

It is true that in written way and/or formal speech the subject is put , but I can tell you that everyone in normal day speaking do not use pronouns, if you are asking someone, he/she will understand the meaning. In fact sometimes it sounds weird if you say the pronoun ' Mañana yo voy al médico' > 'yo' here sounds unnatural and unnecessary. In this case only 'que' works, because it's working together with 'quieres' -> '¿Quieres que lleve algo? (Do you want me to bring anything/something) , is different that ' ¿Que quieres que lleve? (What do you want me to bring?) -> Notice 'qué' has an accent , which it has because it´s acting like a question particle, in that case you could use other question particles like: ¿Cuál quieres que lleve? (Which one, choosing from a group) ¿A quién quieres que lleve? (who do you want me to bring/take) ¿Cómo quieres que lleve (algo)? (How do you want me to bring (something)?) ¿Cuánto quieres que lleve) (How much do you want me to take/bring?) Notice how the structure is always: 'question word'+ 'quieres que'+ 'lleve' Hope this helps

Hey! The phrase means 'Do you want me to bring something?" so if you use the right subject, it would be 'Quieres que YO lleve algo?" so it's correct the conjugation 'que yo lleve'.