Be sure to award such efforts with delighted enthusiasm. Then suggest acting out a verse, a stanza, or the entire poem. Ask your child to make a face of the way the character in the poem is feeling. Remember that facial expressions bring emotion into the performer's voice. Again, be an enthusiastic audience for your child.
Applause is always nice.
If your child is comfortable with the idea, look for a larger setting with an attentive, appreciative audience. Mistakes are a fact of life, so ignore them. Poems are often short with lots of white space on the page. This makes them manageable for new readers and helps to build their confidence. It's important to read to your children, but equally important to listen to them read to you.