Should I come to my partner's first prenatal visit?

Yes, unless it is logistically impossible.

Being newly pregnant can be an emotional experience, especially if you have (or she has) been trying to get pregnant for a long time, and even more so if you have been trying not to.  You should be there to support if a shoulder is needed, encourage if a smile is needed, and just be present if your company is needed.

Let's assume for the rest of this post that the pregnancy is a welcome event.

Beyond what she, the mother, needs, the first prenatal checkup is usually where the pregnancy is confirmed, and you will hear the baby's heart beat for the first time.  This is really neat, and if nothing else, you should be there for this moment: the moment you receive proof that inside this lovely woman is another life.

This is also a good time to interview your midwife or doctor to make sure you get along on a very basic level.  Do you "gibe?" Do you feel good about this person?  Forget the day of delivery -- in a hospital environment, it is a toss-up whether or not this person will attend the actual birth -- what matters now is that you will spend quite a bit of time together.

Taking a typical low-risk prenatal visit with an obstetrician (duration of about 15 minutes) and the timeline of maternity care outlined by Drs. Sears, assuming the first prenatal visit is at 8 weeks gestation as noted by BabyCenter (not unlikely, as your missed period is at 6 weeks), you will spend approximately 2 3/4 hours locked in a room with this midwife or obstetrician. And that is a conservative estimate.

Here's the math:
One visit per month from weeks 8 to 28 = 5 visits
One visit per 2 weeks for 8 weeks (weeks 28 through 36) = 2 visits
One visit per week until born (weeks 36 to, say, 40, which is average) = 4 visits
Total visits = 11
Visit length is 15 minutes each, times 11 visits = 161 minutes = 2 hours, 41 minutes

In conclusion, yes, take the time off of work and join your partner on her first prenatal visit.  Yes, go -- be supportive, be present, and be positive.

Amendment

A note about the case of miscarriage:  If  you attended the ultrasound to confirm the pregnancy and see the heartbeat, you should also attend the ultrasound to confirm the miscarriage.  Remember that you are in this together.  Because it is "we're pregnant," (not "she's pregnant") then it is also "we miscarried."  She did not miscarry alone.  When you attend the latter, more difficult, ultrasound with her, it will help her see that.