I can understand very well your feelings and your great desire to be with you wife immediately after your marriage.
I suggest you go step by step and a bit slowly. I guess you will need to get your marriage contract attested by the relevant authorities and also by the Qatar Embassy in your country. Once you have done this, I do not see any problems in you bringing your wife here even if she has a different surname of her passport. However, I believe a Tourist visa may prove to be on the costlier side for you. Try to go for a visit visa or a visa on arrival if possible. I suggest you also take the guidance of your embassy here on this matter.