It really depends on your circumstances and the child - which only you can know really. I had exactly 2 yrs between DD1 and DD2 and 2 yrs 2 months between DD2 and DS. I never needed a double buggy or a buggy board (i had a buggy board when DD2 ben, but DD1 had one outing on it (which nearly killed me pushing the pram) before DH accidentally broke the fastenings when trying to collapse the buggy with the board still attached.
I did walk a lot with DD1 before DD2 arrived to get her a bit more in the habit of walking places before DD2 turfed her out of the buggy!
In the very early days both times I often carried the new baby in a sling so toddler could go in the buggy. Then later toddler walked and baby in buggy. I usually had sling with me in case, but I only remember one particular circumstance where I had to do a swap over as toddler refused to walk. DD1 started nursery a couple of mornings a week when 2.6 (and DD2 therefore 6 months) and that was a 15 min walk and and we never really had issues with her walking there and back (a few 'moments' certainly, but patience and waiting meant she soon learned that if she wanted to get home for lunch she would have to keep on walking).
After DS born DD1 started reception at age 4.6 and DD2 started nursery at 2.6, for us a double buggy would have been useless as to get DD1 to school I had to go on a bus - in London at busy commuter time, not a hope in hell that I would have got ANY buggy, double or single, on a packed rush hour bus, so DD1 and DD2 walked to bus stop (with DS in sling) then bus, then walk at other end, then once I had dropped DD1 we had another walk on to the nursery with DD2, then all reversed at home time. All the children adjusted perfectly because that is just what we did. Everything is habit really.
I don't think DS went in a buggy after about 18 months - we were all so used to walking by then I could never be bothered to dig out the buggy. I had a hip sling so if he got tired or grumpy I could pop him in, and then he would want to get out again and walk, so he was really independent v early on.
So what I am trying to say in a v round about way is that it depends on your circumstances and pressures. At that time I wasn't working, so was rarely in a particular hurry and could cope with the vagaries of pottering along with a toddler until they adjusted to the routine - which not everyone does have the time for.
Most important thing is to make life easy and best for your circumstances.