Can I major in early childhood education and get a masters in TESOL, and then teach ESL?

You can teach ESL with a Masters that includes TESOL (mostly for teaching immigrants to an English speaking country), but I would get a CELTA which is an actual qualification (from the University of Cambridge) as most schools look for this.

A number of colleges and universities give graduate students the option of earning dual master's degrees, you can do that with Early Childhood Education and TESOL. In a dual master's degree program, a student will earn two master's degrees concurrently. A Master's degree in Teaching of English to Speakers of Other Languages (TESOL) is extremely valuable in education today. The number of students who are English language learners is increasing every year, making it essential for schools to have teachers who are educated to meet their needs. A degree in TESOL can be used all over the world. People from every country are learning English. This degree opens up opportunities in the United States and in other countries to teach English. Many countries have year-long programs in which TESOL educators live in these countries and work teaching English.