Will it hurt you to leave a tenure track position (for another) after one year?
Before committing to leaving, it might also be beneficial to re-consider the current job situation. You mentioned the reasons for leaving are:


  more related to
  
  
    
    the teaching load, 
    the types of classes I'd be teaching, 
    the background of the students I'd be teaching, 
    and the possibility of advising PhD students.
    
  


Regardless of which aspects of each of these items you consider problematic, it appears your fundamental assumption is that all these things will be different in the new job.  Until you actually do get the new job and let these four elements play out as they may, this will remain an assumption. 

Even if you believe the situation will be different based on some 'inside knowledge' at the universities/departments you are applying to, these are merely perceptions and beliefs at this point. There is simply no way of knowing what the new situation will be like until after the fact. 

In the world of tenure-track academe, these assumptions seem risky.

Based on what I hear from peers working in the academe, and occasional reading, your issues are not unique, but are endemic to the professional lives of junior faculty in the academe. 

With this in mind, the problems you are facing may be reframed as truly excellent opportunities. As the likelihood of these issues resurfacing in your career is high, what better way to prepare for this reality than wrestle with it a bit during the first years on the job? I can hardly imagine a better means of gaining invaluable experience and proficiency in dealing with these problems! 

See how you might address these issues now. Whether you succeed or not in changing some things to your liking, there will be valuable lessons learned regardless. The process of this learning might involve struggle and compromise, but the result is you will become a better-heeled junior faculty member, potentially capable of mentoring other peers on such matters or becoming (with time) a change agent after spending time in the trenches and earning credibility in these matters among your colleagues. 

These are not simple or quick lessons, but they may be things are will pay of time and again over the course of your career in the long term. After all, your initial years on the job are not an end but a means toward something even more fulfilling later, correct?

As you see, I got stuck on your initial assumptions before even getting to the questions at hand. But I believe it is well worth to dwell some more on the reasons for leaving, prior to investigating the pros and cons of the actual decision to do so...

What if the same issues crop up in the new job? You will be left with a strange-looking one-year-long stint in a tenure track role, stuck forever on your CV. 

The fact that neither salary nor personal conflicts with colleagues are causing any problems is also not to be taken for granted. Entering a new organization always carries risk of new "people issues" (conflicts related to personality aspects/working style/opinions/character/attitudes/integrity/whatever). I would count my blessings to be in a workplace where these are not major issues. Perhaps you don't even realize how lucky you are! For these reasons, I hope you might be willing to re-evaluate your current position prior to making the decision and evaluating it purely on the groups of career move timing.

Bottom line: Unless the issues you mentioned are absolutely killing you, and you just can't do it any more no matter what, then I guess there is little choice but leave. In which case the question you ask are a mute point. But if you can see some promise in that these experiences might pay off in the long term, then I would encourage you to stick it out a little longer. 

After all, what does a year after which you leave a challenging job say about your ability to persevere, adapt, and succeed despite hurdles? Not too much. On the other hand, getting a few years under your belt in less-than-ideal conditions, and potentially being on the forefront of improving the situation for yourself and your colleagues, will say a whole lot about your professional character. That is worth the time served, in my book.

Good luck!