Natural Gas Analyst Path to Trader

Hi all, earlier this month I started as an analyst on a natural gas trading desk for a large IPP. I work directly with traders and work on market fundamentals. I am pretty early career and I had a couple of questions:

(1) Is it worth trying to make trader at first, rather than switching to the prop-side at a trading house/fund as an analyst first? Not sure where on the industry prestige/recognition scale my company is, but it is one of the heavy hitter US IPPs (in the >10 fleet GW range of companies) 

(2) Is there a point to trying to get into TDPs at this point now that I'm an analyst on a trading desk? Or is it sufficient to perform well and try to go for internal move to trader?

(3) I think down the line I want to trade power and not gas. Do a lot of moves from gas to power happen and have transferrable skills, besides the obvious coupled nature of their markets? 

(4) Is it okay that I never had a scheduling background? Seems on LinkedIn that most gas traders scheduled at some point in their careers. It doesn't seem like analyst to scheduler is an upward move at my company, but also don't want to get pigeonholed as an analyst.

Thank you!