Begonias are generally considered to be toxic.
This website has a lot of great information:
http://www.pawsdogdaycare.com/toxic-and-non-toxic-plants/begonia
The site mentions:
- the underground portions are the most toxic
- "the toxin amount is relatively low, so potentially life-threatening or serious intoxication of a pet from begonia (while theoretically possible) is basically unheard of."
- "towards humans, the University of Nebraska Cooperative Extension in Lancaster County lists begona as non-toxic, with the notation “that these plants have shown no more toxicity than an equal amount of vegetable matter. Symptoms are unlikely”."
- "In most cases of calcium oxalate ingestion, treatment can be managed at home. Upon finding out that your pet may have ingested a plant containing calcium oxalate; the mouth should be rinsed and flushed thoroughly with water. The animal can then be given yogurt, milk, cheese or any other source of calcium to provide relief from the pain, by possibly precipitating some of the calcium oxalate crystals."
I would keep a close eye on your beardie, but I am sure he will be fine!