The Big Love Rocket is probably the single rarest obtainable mount in the entire game, so let's just start off by saying that it's very unlikely that you will get it. However, some people get lucky, so let's just start with the guide to how to get the Big Love Rocket.
You can only get the Big Love Rocket during Love is in the Air world event. The exact date for this event varies, but it is always at the first half of February each year. It lasts for two weeks, so you only have 14 chances to get the mount of each character, since you can only do the event once per day.
Anyway, to get it you need to sign up for the boss event "Crown Chemical Co.". You sign up the same way as you sign up for other groups (default hotkey I), and select your role. Each encounter should only take a minute or two.
All characters that are level 98+ will get a Heart Shaped Box when they complete the encounter, and this has a 0.03 % chance to drop it. You can run the encounter on all your characters as long as they are level 98+, but anyone that is lower level will get another box from the encounter, and this cannot contain the Big Love Rocket mount.
You used to be able to run the event with lower level alts in the past, but as stated above, you now need to be level 98+ in order to get the chest which can contain the mount.