Should a Ph.D. be done with a low h-indexed professor
Picking a PhD supervisor based on his h-index is like picking a car based on his horse-power; you ignore a huge number of factors that are probably equally important if not more. It is drivable (can you work with this person?), is it expensive to run (do the guy needs to pampered and treated like royalty?), are other owners happy with their purchase (are his other PhD students happy with his supervision?), etc. etc. Getting a really fast car only to crash it cause you can't drive it does mean much and getting a supervisor who after a year's time makes you want to quit your PhD doesn't mean much either. Most probably in both cases people are going to think less of you.

I think the most important thing is that you say that "I have started to dislike my professor too." that is a major problem and you should not pick a supervisor that you dislike. I do not mean that by being "homies" with supervisor; I mean about mutual respect and ability to work efficiently and with understanding about each other maybe "small quirks". (eg. My supervisor avoided setting up morning meeting with me because I am a night-person; it was fine, he even joked up about it at times "Next week I have X thing going on so we probably need to meet at 11.00. I know you'll just be out of bed but that is my only available time." That did not mean though I was not expected to be always punctuational for our meeting or having worked seriously on the projects at hand.

To recap: As you present things I would say "do not to work with this professor" but not because of his low h-index but because you say you do not like him and that his PhD students seem not to take good positions (low after-sales value :) ).

You mention that US institution are out of the equation effectively; "fine". Have you thought of PhD programmes in Europe? Some small, not too famous but reputable universities in EU can be stepping stones for a post-doc in US  (Given you do excellent work at your PhD obviously).