Yes, that is a new plant forming, but don't separate it yet. It needs to form some roots while still attached to the mother plant. Is the mother plant still ok?
If you just mist it with a spray bottle daily, you should see roots forming pretty soon. When they're a couple of inches long you can cut the stalk below the baby and stick it in a pot of orchid medium (not soil!).
A little bit of soluble fertilizer in the misting water will help things along too. Just make sure there's no water sitting in the cup of leaves. You might remove the stake in the pot (which is meant to hold the flowers upright) to let the plant take a more normal posture as this will let that baby plant drain.
Phals grow in nature on vertical surfaces with their leaves hanging down, and the flowers are meant to cascade, not be upright like you find them at the stores.
