Best time to Rajasthan is from Mid October to end of March. Bcos once heat starts setting in, it becomes difficult to travel and also becomes an issue to book hotels as it gets difficult to stay without ac. But in the winter months, though it is the peak season, one always has options to find pocket friendly places in and around various parts of Rajasthan including Jodhpur, Udaipur, Jaisalmer, Bikaner, etc.
but also be aware that this is the time too much travellers are also flocking around the place and tourist attraction are usually crowded. Hope this helps.
October is the beginning of winter here in Rajasthan, So it will eventually gonna be one of the best times to visit Rajasthan. Specially the camping in Jaisalmer and apart from that you are gonna love the Rajasthani 'Dal, Bati, Churma'.
October is ok to visit but if you are concerned about heat, then better plan it between November - January. October is the time when weather starts changing and if you have plans for Jodhpur, Udaipur, Jaisalmer then it might be little difficult to explore in day time. If you have any query or need help in planning, do ping me as I have been to Rajasthan couple of times.