Live MTT hand from lastnight. Right move?

[joshgill17]

$80 buyin w/rebuys event last night with around 60 players. Down to 15 players and I'm sitting on around 18,000T which is about double the avg stack. (Started with 2000).

Blinds are 1000-2000 and I'm on the BB.

Player in middle position min raises to 4K. Two callers and it's back to me. I look down at red kings.

Reads: original raiser is solid, but predictable, although he plays a lot of hands. first caller is a calling station and the 2nd caller just arrived at our table so no real reads. I have everyone covered except for the raiser who has about 3000T more than I do.

Obviously I am raising in this spot to get it heads up with the original raiser. His range of hands is 1010-AA, AK. I put at least one of the callers on A and face types of cards, or small PP.

So we have around 19K in the pot + antes. At this point I contemplate making it 12K but decide that the best play is to push all in. Is that the correct play or do I raise to 10-12 and push any non ace flop since I'm first to act. I felt I was pot committing myself with a reraise and wanted to try and take it down right there or play it heads up.

Correct push?

Results to come.