Princess Eugenie of York opted for an elegant autumnal outfit for her first public outing since announcing that she and her husband Jack Brooksbank are expecting their first child in early 2021.

In pictures published in Daily Mail, Princess Eugenie was seen rocking a black pleated dress as she left Harry's Bar in Mayfair, London, after grabbing lunch with her brother-in-law Edoardo Mapelli Mozzi on Tuesday. The mini dress featured a belt tied under the bust allowing the fabric to settle over her blooming baby bump.

The 32-year-old teamed the frock with a gorgeous teal coat by French label Maje, black leather boots, black tights, and a black leather bucket bag which she slung over one shoulder. She also sported a printed face mask which she was wearing on her last outing as well.

The British royal, and her older sister Princess Beatrice's husband, were joined by another friend as they went for a stroll after lunch at the upmarket Italian restaurant.

The younger daughter of Prince Andrew and Sarah Ferguson, the Duke and the Duchess of York, announced the baby news through an Instagram post earlier this month. Betting sites have already started predicting the gender, name, and birth month of the future royal baby.

It's a popular opinion that Princess Eugenie, granddaughter of Queen Elizabeth II, will pick a traditional royal name for her firstborn. Betting site Betfair has two frontrunners for the baby's name- Arthur if it's a boy and Alice if it's a girl, reports Hello! magazine.

"Punters seem to think that a traditional royal name is on the cards, and Alice and Arthur lead the betting as 8/1 joint-favourites," Betfair spokesperson Darren Hughes said.

The names in the running for a girl also include Diana, after Eugenie's late aunt, at odds of 20/1. Other predictions are Celia at 10/1 and Augusta at 14/1. Meanwhile, Henry and Thomas are popular names for boys running at odds of 10/1 and 14/1 respectively. Boris is unpopular at 200/1.

A very few have placed bets that Eugenie will name the baby after her elder sister Princess Beatrice. The name is running at odds of 100/1. Other possible baby names are Victoria at 18/1 and Albert at 20/1.

The betting firm has also seen bets on the birth month of the future royal, with January being the frontrunner at 11/10. February has odds of 2/1, March is at 5/1 and April is 10/1.

Meanwhile, betting site Coral saw a few bets placed on Andrew, after Eugenie's scandal-hit father. The firm's spokesman Harry Aitkenhead told the Daily Star: "Although we haven't seen many bets on Andrew, there have been a couple of punters place small stakes on it. These are only £1 or £2 bets, as is often the way in markets like this, and a £1 on Andrew would return any lucky punters £100 winnings if their predictions came true, with odds of 100-1."

"We always include any family names in our betting for each Royal and there is always a wide range of choices from bettors having a flutter," he added.

Arthur continues to be a favourite at this site as well, as Aitkenhead said: "Arthur is a name that appears in Jack's family history, as well as the Royal family, so we think it could be the perfect one for the their first child if it does turn out to be a baby boy." For a baby girl, the site has Mary, Lily, and Alice among the most popular names.

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Princess Eugenie and Jack Brooksbank attend the Chelsea Flower Show press day at Royal Hospital Chelsea on May 23, 2016 in London, England Heathcliff O'Malley - WP Pool/Getty Images

Betting intelligence sites Mybettingsites.co.uk and Ladbrokes also announced Arthur as their frontrunner. The punters have also placed bets on the gender of the baby as well, with a boy being the popular opinion.