Can a spouse give "solely" owned real estate to the other spouse?

No quitclaim deed here. A quitclaim is generally used to give up one's partial ownership interest in property. If she owns it 100%, she can execute a full warranty deed to you. You should probably consult an attorney that specializes in estate planning to see what's the best way to go about this, either a sale for a nominal fee or an outright gift. There can be tax implications for both. I do not see any reason for this, because all she has to do is update her will to state that the property passes to you at her death. You would receive it then at its market value at the time. Receive it now and your basis is her cost or possibly less. See a good attorney first.