Reality TV star Anna Nicole Smith, her photojournalist ex-beau Larry Birkhead and their lawyers are awaiting a ruling on whether the court will order that a paternity test be done on Smith's newborn daughter to determine whether Birkhead fathered the child.

Smith has not complied with Birkhead's requests for a test on the infant, 3-month-old Dannielynn Hope Marshall Stern, saying the baby's father is her lawyer and current boyfriend, Howard K. Stern.

So Birkhead filed a lawsuit and the hearing went forward Wednesday morning, after Judge Robert A. Schnider denied Smith's request for a delay in the proceedings.

Schnider is expected to issue a written ruling this week or early next.

The hearing was held at Los Angeles Superior Court and lasted about an hour. Birkhead and his attorney Debra Opri were present; Smith was not.

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"Hopefully, within a month or so, the order goes forward and it will be enforced and Larry will be proven the father. I have every confidence in that," Opri said Tuesday on FOX News Channel's "On the Record With Greta Van Susteren." "The lady doth protest too much. It's despicable. It's costly ... And ultimately, she will give the test. Ultimately Larry Birkhead will prevail."

In October, Birkhead filed a second lawsuit against the former Playboy Playmate, this time alleging fraud and conspiracy. He had earlier filed a lawsuit in Los Angeles seeking a court order to demand Smith, who is currently living in the Bahamas, bring the baby to California for a paternity test.

Click here for the Anna Nicole Smith Celebrity Center

In the second lawsuit, Birkhead alleges Smith provided fraudulent information when applying for her daughter's birth certificate in the Bahamas. Smith identified Stern as the father.

The lawsuit asks that Stern's name be deleted from the girl's birth certificate and replaced with Birkhead's.

"I am the father of Dannielynn and I think this is ... a crime," Birkhead said in October. "I expect to be reunited with my daughter with the help of my attorneys."

Smith's daughter was born Sept. 7. Three days later, Smith's 20-year-old son, Daniel, died while visiting her in a Nassau hospital.

"This would have been Larry's first Christmas with his newborn baby girl, and he's upset," Opri told FOX. "It's hard on him. His heart is breaking."

FOX News' Catherine Donaldson-Evans and The Associated Press contributed to this report.

Click here for the Anna Nicole Smith Celebrity Center