If it's a laser pointer made with a red (670, 650, 635 nm), blue (445 nm), or violet (405 nm) laser diode, there's absolutely no infrared emitted.
If it's a properly made diode-pumped solid-state laser pointer (532 nm green, 473 nm blue, 404 nm frequency doubled violet) there's an infrared filter in the optical train which removes the large amounts of invisible pump light and leaves only the visible green.
If it's a crap green laser pointer (e.g. the "high power" green pointers sold on eBay and the like) then there is a real possibility the manufacturer omitted the IR filter to increase profits and/or the balloon-popping potential of the pointer. Check with a laser power meter and an IR-passing filter to verify the lack of IR output.
If no such tools are available, use a camera sensitive to infrared, block the visible beam with a filter, and check that no IR is coming out. IR-passing, visible-blocking filters around the house include the tinted plastic windows on remote controls and the front panels of remote-controlled devices, exposed color photo film negatives, and the disks of coated Mylar film inside floppy disks. Those last two should never be used as filters to observe the Sun due to the fact they totally pass IR and you can cook your retina in seconds without realizing anything bad is happening.
Infrared leaks may not be collimated like the green beam and will be visible (on camera) as a beam, cone, or ugly spray of light coming out of the filtered device.
There are reflected light hazards to worry about with all lasers. For example, shining the laser onto a smooth or polished floor in the direction of your pet will result in some light making a dot on the floor and most of the light bouncing off into your pet's eyes. If you can see the laser's reflection light up your pet's face, you may be causing eye damage.
If it's a high-power laser pointer (output over 5 mW) you are being carelessly negligent in its operation if you're waving it around in any situation where people or animals can get hit in the eye with its beam. Safe eye exposure is probably much less for cats and dogs due to the presence of a tapetum lucidum which concentrates light hitting their retina, their much larger pupils which take in much more light, and active suppression of the blink/turn reflex due to the fact they're chasing that dot and don't want to look away from their quarry.