in your price range from Canon, Sony or Panasonic (even JVC) will perform similarly.
We assume you don't need a tripod, audio gear or cases.
Generally speaking, larger lens diameter and larger imaging sensor (better yet, a 3-chip sensor "system" 3CMOS or 3CCD) will provide a wider "window of opportunity" associated with lower levels of light.
bhphotovideo searched camcorders priced between $800 and $950 resulted in the Panasonic HC-WXF1 and Sony FDR-AX53. Both are 4k, have their built-in lenses (traditional camcorder), have optical zoom (and digital zoom which should not be used unless very sparingly).
Both have a 1-Chip 1/2.5" CMOS sensor. For a single sensor, at the consumer level, this is large.
The Sony has a built-in infrared emitter for monochrome video capture using "NightShot" mode. Panny does not.
Both have audio input and headphone jack. The Panny has a cold shoe accessory mount, Sony's is a hot-shoe for Sony-proprietary add-ons (which you don't need).
We don't know which camcorder model you are currently using, but it is possible batteries from the current camcorder will work with the new one.
We don't know if you want to edit the captured video. 4K video suitable for editing can be a computer hard drive hog. XAVC (in my opinion) is the preferred recording format (Sony does this, Panny does not) and is closer to "pro grade". MP4 is OK- may be "good enough" for your needs (Panny does this, Sony does not).
Check your video editor for the 4k formats it can use.
What cameras do you recommend for live theater performances and dance performances? I am looking for a 4k, low light camera. It has to be camcorder/ no lenses, zoomable. I have been using older sony camcorders but the issue I've been running to is that it is terrible at low light when I am recording a dance performance. Along with that, the senor hates purple and blue, when recording something with blue or purple light it becomes over saturated and pixelated. It a 5-year camera, I need a new one, can anyone help me? My price range is the 1,000 $ mark.