Borax is sometimes used as a poison for Creeping Charlie, and less often as an insecticide so this should tell you that it can cause injury or death in plants and animals - at a sufficiently large enough dose. Borax is also used in home remedies so clearly it isn't always fatal, or even harmful in appropriate doses.

I don't know where or how you want to use this naturally occurring mineral, or how your pets could come into contact with it but according to the National Pesticide Information Center here is some information about a toxic dose of Borax:

Signs of Toxicity - Animals

• Ingestion of small amounts of boric acid or borate salts by animals has resulted in clinical signs that include excessive salivation, thirst, fever, vomiting, retching, depression, loss of appetite, diarrhea, and abdominal pain. The vomit or stools of exposed animals may contain blood or have a blue-green color.15,16
• The onset of clinical signs following boric acid or borate salt ingestions is usually within 2 hours.16
• Following ingestion of large amounts of boric acid or borate salts, animals have also shown signs of ataxia, tremors, seizures, decreased urination, and can develop reddish-violet colored skin. Suppressed growth, reproductive sterility and testicular degeneration in males have also been observed. Seizures from massive oral ingestions of boric acid can be followed by depression, metabolic acidosis, coma and death.12,15,16
• Signs reported in animals following the chronic ingestion of boric acid include anorexia, weight loss, vomiting, diarrhea, rashes, hair loss, anemia, kidney damage resulting in difficulties urinating and death.15
• Dermal exposure to borax has resulted in redness or inflammation of the skin.16
• Boric acid and disodium octaborate produce mild eye irritation but sodium tetraborate (borax) is highly irritating to the eyes.11
• Older animals or young animals may be more sensitive to boric acid and borate salts than adult animals.15

I hope this is helpful.  Please contact AaE again if you have further questions.