The correct option is
A am travelling
The clue for the answer is in the second sentence. The words, "have+got" ('got' is the past participle of the verb 'get') in the second sentence convey that it is in present perfect tense. It conveys that certain travel arrangements (booking flights and reserving hotels) have been made. This suggests that the first sentence talks about a travel which is yet to happen. Hence, the first sentence is in future tense.
Option A: The present continuous form, "I am travelling" refers to the future due to the words, "this weekend". It indicates that the speaker has already decided to travel to Srinagar this weekend. Hence, this option is correct.
Option B: The phrase "I travel" is in simple present tense which conveys that the speaker regularly travels. This cannot refer to a future event which is to happen at a specific time i.e "this weekend". Hence, this option is incorrect.
Option C: The phrase, "I going to travel" is grammatically incorrect as the auxiliary verb, "am" is missing. The correct usage would be: "I am going to travel". Hence, this option is incorrect.
Option D: The phrase, "I would travelling" is grammatically incorrect as the auxiliary verb, "be" is missing. The correct usage would be: "I would be travelling". Hence, this option is incorrect.