I am a 5"5' 150 lbs female and I drink fairly regularly (about 2-3 days a week). Yesterday I consumed 3 12oz beers between 6 and 7pm and had 1/4 a beer around 11pm. I had to give a urine sample this morning at 10:30am. Will the alcohol show up on my drug test?

Alcohol (EtOH) probably would not. If the UA is screened for EtG/EtS there is a very high probability that it will.

According a calculator found here:

Toronto criminal lawyer for impaired driving

You should have had 0 BAC (Blood alcohol content) by the time you gave the urine sample.

Keep in mind this isn't an exact science however.

Thank you very much! If it is just a pre-employment drug test given at a hospital, what are the odds that it will be an EtG test?

Very slight. In fact most pre-employment tests are simple 5-panel screens looking for illegal drug use and don't check for alcohol at all. In addition, the presence of EtG shouldn't be a disqualifier even if tested for as it indicates past consumption and not impairment.