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I would wait until it is 91 days and your third statment cuts, that is usually how Navy works most of the time. There have been exceptions but not many and with your intial low SL I would not attempt anything until after your thrid statement cuts and Navy has issued the AR fico scores for October.
I would wait the 3 weeks until your 3rd statment hit then apply for your second card.
Ask the question: Is there a need for a second card right now?
Is it possible to wait?
I waited nearly 6 months; requested a $10,000 cli on first card, Cash Rewards, instant approval.
Immediately app'd for second card AMEX, instant approval $25,000. SL
If there is no immediate need, waiting another month or two, allowing your credit to "cook" and continue to improve may net you greater success.
Your choice- obviously but without the need for another card right now, as Elton John says: things can only get better..
♪♫♪Don't look at it like it's forever
Between you and me I could honestly say
That things can only get better ♪♫♪ ~Elton
Good Luck whatever you decide..