I had to leave my software engineering career for a couple of years to help with a family business. When I was ready to go back to my normal profession, I found it difficult to find many jobs to apply for as my local job market for my particular niche was quiet at the time. So 4 months ago I took a low paying position with a small local startup company to start getting industry experience under my belt again. But while the people are very pleasant to work with, as a startup they don't have much money and the salary is far below my normal expectations and definitely too low for me to be able to stay long term. I really want to make the market rate for my experience level and I am now seeing that there is a pickup in my area for my speciality with the larger and better paying companies and I want to apply to them.

In interviews, I imagine I am likely to be asked why am I looking to move on again so soon from a new job that I've been in for less than 6 months. What should I say about the reason? Should I openly say its because of below market rate pay in my current company?

And if I admit to the interviewer that I'm currently making 
below current market rate, I'm concerned they might attempt to offer me something in between my current pay and current market rate so I would undermine myself.

Is there a way to answer such a question so that it wont raise a red flag that I am leaving a new job so soon and I don't undermine my goal of being offered market rate?