Layla, who weight 58 kilograms (128 pounds) when she was born Jan. 23, is developing well and drinks up to 20 liters (5.3 gallons) of milk a day.
Layla currently weighs 138 kilograms (304), zoo officials said.
The zoo had let the public pick the female calf's name from five choices. Layla, originates from Egypt and means "born at night."
Zoo visitors were watching intensely as caretakers opened the door to lively, unshy Layla's stall.
"Look at her, she is just like a little (human) baby, so adorable," said zoo visitor Istvan Zsarnoczay.
"Constantly moving, she just can't stop," a female visitor said.
"All of this is so new to you, isn't it? You just have to look at everything," said nine-year-old Fruzsina Jeravek, who came to see Layla's debut public performance.
The zoo said Layla's first few weeks were rather uneventful but she would gradually become vivid and playful. "In the first weeks, the little one almost exclusively ate and slept. Then it became increasingly active and now she loves to play catch with her caretakers."
On Thursday, Layla took her first sniff of fresh straw and grass in the enclosure and she seemed to love it.
Prancing and skipping through the dust she showed no fear of the crowd and was rather playful with the media.
"Look at her - she is playing with the cameras," a visitor said.
Mother Lulu, 26, who failed to conceive naturally when kept with a male, became pregnant in 2005 after a group of veterinarians from Germany, Austria and Hungary started insemination. Baby rhinos are carried for about 16-17 months.
Lulu underwent insemination again in February - only a month after giving birth - as fertility levels are highest in female rhinos right after they have delivered calves, the zoo said.
Veterinarians for Lulu's second insemination used the sperm of Simba, a male rhino from the zoo in Colchester, Britain. Results on whether Lulu was pregnant would soon be known.
The proud mum was not present when Layla was presented to zoo visitors.
Although she has been protective of her newborn she has failed to nurse her, officials said earlier and added she had at times turned aggressive - initial refusal to feed was natural with inexperienced mother rhinos.
Layla, who loves to play tag with her caretakers, is currently being fed by zoo workers. She was carried for 16 months and 15 days.