Hi, that's a very good problem! I think you are on the right track, because it is possible, using some of the reactions shown below, to take your enol product, 1,4-cyclohexadien-1-ol, and get to the final product 2-cyclohexen-1-one.
In your mechanism, you formed a vinylic carbocation. The stability of a 2° vinylic carbocation is comparable to that of a normal 1° carbocation, and as such, its formation is not very favorable. I can't rule it out entirely, but in the following mechanism, I used an alternate pathway not involving a vinylic carbocation, by starting with electrophilic addition of H+ to the double bond that has the methoxy group present. This could occur in competition with protonation of the methoxy oxygen, but if the vinylic carbocation cannot form, protonation of the oxygen would be a dead end. Here is a (proposed!) overall mechanism:
Shown in the first line, the resulting carbocation from addition of H+ to the double bond is stabilized by donation of the oxygen lone pair, spreading the positive charge out over two atoms. Thus, this may be a relatively favorable initial step.
In the second line, addition of water yields a protonated hemiacetal from which we can get to the ketone 3-cyclohexen-1-one (the last compound in line 2). Note that this compound is just the keto tautomer which your final enol product 1,4-cyclohexadien-1-ol would rearrange to (a standard acid or base-catalyzed process).
The third line shows the acid-catalyzed rearrangement of this keto tautomer to the enol tautomer, but this time with the enol double bond on the other side of the OH group, resulting in an enol of a conjugated diene, which should be more stable and therefore more favorable to form (or so my thinking goes!).
Finally, in the fourth line, I first drew the other resonance structure of the previous enol and then protonated it, "trapping" the product, an a,b-unsaturated protonated ketone, which, upon deprotonation of the oxygen, gives the a,b-unsaturated ketone product.
Works on paper anyway! 
Steve
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