You can file for an absolute divorce on the grounds of desertion if the desertion of your wife was a deliberate and final act of ending your marriage, with no reasonable expectation of a reconciliation, and the desertion has gone on for at least one year before you file.
You can file for a limited divorce now if you want to get the court process started on custody, support, etc. You'll just have to amend your complaint to one for absolute divorce after a year since her desertion has passed if you want to get a full and final absolute divorce.
As far as alimony goes, there are numerous factors the Court will take into consideration when determining if alimony will be awarded. One of the factors is the grounds for divorce. So if your wife is claiming that your cruelty towards her is the reason she "abandoned" you, she will have to prove that allegation in the divorce proceeding. But other factors the court will consider are your respective ages and incomes, the length of time you were married, and the standards of living you enjoyed while married compared to being separated.
I would suggest you have a consultation with a domestic lawyer on these issues. If you cannot afford an attorney, many counties have free family law clinics that can help you.