What is your objective for grafting the key lime on the mandarin? They will grow fine on their own roots. To answer your question (if I understand correctly--it is a 1 inch tall seedling)--It would be difficult to get a usable bud for T budding from it by next spring, but you may be able to get a toothpick size scion that you could use with bark grafting. I have used many toothpick size scions on pencil size stock--almost all have taken, but most grow very slowly--a few have done fine.
Normally, young seedlings, or their juvenile buds are not used for budding/grafting onto other citrus trees, as they will not produce fruit for a long time. When a seedling or a bud that is taken from a seedling is grafted/budded onto a citrus tree, the seedling/bud "remembers" it's previous node count number, and "remembers" that it is not a mature seedling/bud. Therefore it will have to grow for some years to produce the proper number of nodes, before it reaches maturity and is capable of fruiting. However, if you remove a mature bud (from a tree that is already a fruiting tree), the mature bud "remembers" that it is capable of fruiting and could bloom the following year. Lastly, although you can bud most any citrus variety onto any other citrus variety, normally lemons and limes are not budded onto mandarins. - Millet
