The early months of Kate Middleton’s third pregnancy have been most challenging, but she’s over the moon over having another baby …

Kate Smiling

Due to hyperemesis gravidarum, a condition that causes severe morning sickness, Kate has been sidelined for much of the past month.

That’s tough for many reasons, but most notably because it caused her to miss Prince George’s first day of school three weeks ago.

Despite being “desperately sad” to miss her first-born’s “special milestone,” a palace insider said her latest doctor’s visit lifted her spirits.

And for very, very good reason:

According to the physician, Kate and Prince William found out the gender of their third child … and they’re expecting another baby girl!

“They are over the moon,” dishes the palace source, who adds, “Expect the whole family to start celebrating as soon as Kate is up to it.”

Duchess of Cambridge Pic

While the royal family won’t publicly state Kate Middleton’s due date, but it’s believed that she is just over months along as of now.

Given that we learned right after Kate got pregnant with her third, that would put the little one’s arrival date around early March.

In any case, the fact that it’s a girl has everyone abuzz, as “Once Kate told William and the kids, there was little hope for discretion.”

“Kate was overjoyed to have something to celebrate as a family, especially since she couldn’t be there for George that morning.”

She told William in a particularly intimate way, evidently.

While he was 
off taking George to school, the Duchess penned a handwritten note to her husband … in the voice of the new baby!

Kate Middleton and Her Hot Prince

As if that weren’t precious enough, she signed the note using the name they had already chosen if they were to have another girl …

Alice!

When the prince discovered the letter on his desk, he was moved to tears … after which they told the kids, via cupcakes with pink icing.

You can’t make this stuff up. Well, actually the palace insider quoted by OK! here likely did, but you gotta admit, they did a great job.

“George couldn’t stop rubbing his mother’s tummy,” the insider says. “He was too young to understand when Kate was pregnant with Charlotte.”

“But this time he’s excited.”

Who wouldn’t be?! Most of all, the news has been a welcome bit of relief for Kate, who’s battled this same health condition three times.

Kate Middleton in the Rain

Alice, a family name for those who might be interested, is one of Queen Victoria’s daughters and the mother of the Duke of Edinburgh.

Her arrival will be a joyous occasion, as Kate wants “George and Charlotte to participate in making the baby feel welcome.”

As for William, he “desperately wants to keep Kate happy but he worries that she’s overtaxing herself,” the source explains.

“William believes Kate would benefit from having an additional nanny or housekeeper around, especially in these giant new quarters.”

While there has been talk of Kate hiring a supernanny, she says she’s been on being “as regular a family of five as possible.”

They’ll be an adorable one, that’s for sure.