I'm sure you'll have a great time at Inks Lake SP. I checked and could not find a reference to a state-wide "Burn Ban" but I did find the following for Burnet County:
Burnet County Burn Ban
Save you from hauling a bunch of firewood you can't use

. Site also should give you more info about Burnet County. Also, if you have some time you might want to read my ramblings about Inks Lake. At the bottom of the review you'll find a link to pictures I took of the park. Might help a bit.
Inks Lake State Park
If your at the park on the weekend, be sure to try a sandwich from Mike's Texas BBQ. Well worth the cost

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Hope this helps and you have a great trip. Happy Camping!
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Turn Key, DW & Tilly, The Camping Boston Terrier
'03 Chevy 2500HD, 4X4, X-Cab, Long Bed
'04 K-Z "Durango", 275RK ("Sunday Haus II")
Twin Kayaks, "The Ride" by Wilderness Systems
North Central Texas, Where The West Begins!