Any pictures of the flowers?
Likely not D. burkeana
Here is the original description by Planch in Latin:
Drosera Burkeana Planch. — D. pusilla; foliis omnibus
radicalibus, parvis , lamina subrotunda petiolo breviore, subtus
nuda, ciliis glanduliferis ejus latitudinem subaequantibus
ornata; stipulis singulis acute bifidis, basi ima in unam intra
axillarem concretis; scapis 2-pollicaribus, gracilibus, 6-7 floris
calycibusque sparse et minutissime subglanduloso-hirtellis ;
stylis 3, profunde bipartitis ; stigmatibus longe linearibus;
seminibus minutis, eilipsoideis ; testa atra , duriuscula , non
conspicue rugulosa.
Hab. Africae australis subtropicae ditione Macalisberg ; Burke in herb.
Hook.
Habitus Dr. tenellae HBK. Folia, petiolo adjecto . vix 1/2 poll, longa,
lamina diametro 2 lin., petiolus apice excepto nudus. Calyx infra médium
5-fidus, laciniis ovato-oblongis, obtusissimis , membranaceis , sub
anthesi vix semilineam, sub fïuctu sesquilineam longis. Pedicelli inferiores
2 lin. longi , fructiferi erecti. Petala (rosea? ex sicco) in unguem
gracilem longe attenuata. Antherae parvae, loculis oblongis, basi et apice
discretis. Capsula calyce marcescente inclusa, eodem brevior, oblongo-obovata
; placentis latiusculis nec basim nec apicem valvae attingentes.
(Descriptio ex specimine unico.)
Rough translation via Google to English. Some clean up on first few sentences:
Drosera burkeana (Planch). - D. pusilla; all leaves deep, small, roundish leaf with a shorter petiole, underside naked, lamina covered with glandular cilia as long as is wide; stipules each acutely bifid, one inside the base of the lowest in the axillary concrete; scape 2-pollicaribus, slender, 6-7 flora calycibusque sparse and very finely subglanduloso-hirtellis; 3 styles, deep down in two divisions; tattoos very linear; seeds minute, eilipsoideis; black shell, straining, not markedly rugulose. Hab. Africa south subtropical domain Macalisberg; Burke in the herb. Hook. Dr. Habits tender HBK. The leaves, petiole terms. hardly 1/2 Poll, long, blade diameter of 2 lines., petiole apex except naked. Calyx below the middle 5-pentamerous, ovate-oblong, very obtuse, membranous, under the flowering hardly semilineam under the waves sesquilineam long. pedicels lower 2 lines. long, erect in fruit. Petals (pink? From the dry) in the fingernails slender tapered off. Anthers small, a money box oblong, base and apex status. Capsule drooping sepals included, the shorter, oblong-obovate ; placentas extending or reaching base or apex of the valve. (Description of a single specimen.)
D. burkeana should be similar to D. rotundifolia with shorter petioles.