As a short guy how much it sucks to try and date. I'm lucky in that I'm quite tall but man, are women stuck on height. Most women will NOT date a man shorter than them. It is a deal breaker to them for whatever reason. They also seem to feel it is perfectly reasonable, and not just very shallow.
It really sucks for short guys because at least with looks you can generally do something. While you can't change your looks radically you can lose weight, work out, wear better clothes, etc and improve your looks at least somewhat. Also cosmetic surgery is a more drastic approach that can modify some things. There's fuck-all you can do about height though. You are 5'1"? That's what you are.
Women like to think they aren't shallow, and of course some really aren't (as some men aren't) but most are they just lie to themselves about it. One of the issues is that women tend to have a skewed view of men. They believe most men are below average. OKCupid did an interesting study on this. Men rated women's pictures on a bell curve of attractiveness, as one would expect. Women rated most men below average. So what you get is a lot of women who believe they've "settled" for a below average guy and thus aren't caring about looks, when in reality they've "settled" for an average or above average guy and just haven't gotten a hunk.