01/30/2012 04:07 pm ET

Rumer Willis Parties At SAG Awards Days After Demi Moore Was Hospitalized

At least one of Demi Moore's daughters felt well enough to make it to theScreen Actors' Guild Awards after party, just days after her mother was rushed to hospital and treated for some kind of adverse drug reaction.

Rumer Willis was spotted sneaking into the official after party outside the Shrine Auditorium in Los Angeles on Sunday night,reports Us Weekly.

Willis was trying to keep "a crazy low profile," says a source who claims "she definitely didn't want anyone to see her." But for someone wanting to stay out of the spotlight it seems strange the 23-year-old would show up to the party at all -- especially since it's been widely speculated that Rumer was present when Demi Moore started convulsing last Monday.

In the 911 recording released to the press last week, many voices can be heard talking to the emergency dispatcher, and one woman calls out the name "Ru," which is Willis' nickname.

If she was present, the experience hasn't slowed her down. People reports that Rumer was also spotted having dinner with friend Annie Starke, actress Glenn Close, and Close's husband David Shaw on Saturday night. The foursome ordered cocktails and kept up lively chatter, according to the spy who added, Rumer seemed cheerful at times, but kept a tight grip on her phone and frequently tuned out becoming engrossed with a text conversation on her phone.

According to People, Starke and Willis hung out again at the after party on Sunday night, where they sipped Champagne and mingled with other guests. As the party came to a close, Rumer didn't want her night to end, reportedly heading off to famed celebrity hotspot Chateau Marmont.

Celebs on the red carpet at the SAG Awards:

SAG Awards Red Carpet Arrivals