Congratulations on getting this job, it sounds great. I’m sure you will make a difference to their learning.
I suggest you look at books for learners of English. Rhymes such as the one you mention are great fun but as they are intended for native speakers, the language is much more complicated.
Check out what materials are available in the school; you could take songs and rhymes from their usual course book, check with the class teacher how you could share this out. You could also look at jazz chants by Carolyn Graham for young children. A fun song that involves a lot of movement and repetition is:
“If you’re happy and you know it, clap your hands, etc”
Other movements to add, include: stamp your feet / click your fingers / shout hoorah / do all four…. You can change the phrases and even invent your own, depending on whether you want the class to be quiet or not.
Songs and rhymes are fun but they are not the only things you can do. Look also at story books, try to choose books with pictures. With stories, you can be more adventurous with the level of English. Provided you mime and show pictures, students will understand a lot even if they don’t get all the words.
You can also play games of bingo using numbers, colours, familiar objects. If you don’t have time to make the bingo cards, have students do it themselves. Choose about 25 - 30 words that the children know; prepare the same number of cards and write one word each card. Prepare the grids students will use, but don’t fill in the words. Write the 25-30 words you chose on the board, the children choose 6 or 7 of those words and write or draw them on their grid. You are all then ready to play.
You can also use guessing games and adapt common board games for learning English, e.g. snakes and ladders.
If you would like more ideas, you can look through my previous posts and / or write in again.