Is it healthy for a toddler, 3yrs. old, to gain 10lbs in one month?

No: Normal would be ~5 lb in 1 year. Needs to be evaluated ASAP.

Repeat the weight at your Pediatrician's office and compare it to prior weights as recorded on the growth chart, calculate BMI, measure the height. A healthy diet should include 5 fruits and vegetables per day, lean protein sources, and no fast or deep fried foods. Avoid sugary sweets and soda, and please review the need for metabolic testing.