Renting Recent VA Refi - Zillow Mortgage Advice

We have just completed a VA?refi on our current home.? We've lived here for 4 years.? Its feeling kind of small though and we want to purchase a new construction here in town with an FHA loan.
1) Will we be able to do this?
2) will it affect our interest rate on our VA?

Monthly income: 7500, current obligations (including current mort/tax/ins) 1890.

TIA

Source: http://www.zillow.com/advice-thread/Renting-Recent-VA-Refi/469345/

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